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Showing papers in "Journal of the American Statistical Association in 2015"


Journal ArticleDOI
TL;DR: In this paper, the authors formally study the most common regression-discontinuity (RD) plots based on an evenly spaced binning of the data, and propose several data-driven choices for the number of bins depending on the goal of the researcher.
Abstract: Exploratory data analysis plays a central role in applied statistics and econometrics. In the popular regression-discontinuity (RD) design, the use of graphical analysis has been strongly advocated because it provides both easy presentation and transparent validation of the design. RD plots are nowadays widely used in applications, despite its formal properties being unknown: these plots are typically presented employing ad hoc choices of tuning parameters, which makes these procedures less automatic and more subjective. In this article, we formally study the most common RD plot based on an evenly spaced binning of the data, and propose several (optimal) data-driven choices for the number of bins depending on the goal of the researcher. These RD plots are constructed either to approximate the underlying unknown regression functions without imposing smoothness in the estimator, or to approximate the underlying variability of the raw data while smoothing out the otherwise uninformative scatterplot of the da...

326 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher.
Abstract: Weighting methods that adjust for observed covariates, such as inverse probability weighting, are widely used for causal inference and estimation with incomplete outcome data. Part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes, or a variety of population means for several variables. However, this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings. To address these limitations, this article presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher. This method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions, such as variances and correlations and also, for example, the ...

314 citations


Journal ArticleDOI
TL;DR: In this paper, a new class of Dirichlet-laplace priors, which possess optimal posterior concentration and lead to efficient posterior computation, is proposed, which can be expressed as global-local scale mixtures of Gaussians.
Abstract: Penalized regression methods, such as L1 regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimensions. This has motivated continuous shrinkage priors, which can be expressed as global-local scale mixtures of Gaussians, facilitating computation. In contrast to the frequentist literature, little is known about the properties of such priors and the convergence and concentration of the corresponding posterior distribution. In this article, we propose a new class of Dirichlet–Laplace priors, which possess optimal posterior concentration and lead to efficient posterior computation. Finite sample performance of Dirichlet–Laplace priors relative to alternatives is assessed in simulated and real data examples.

308 citations


Journal ArticleDOI
TL;DR: In this article, the authors report results of two randomized controlled trials of near real-time epidemic-type aftershock sequence (ETAS) crime forecasting, one trial within three divisions of the Los Angeles Police Department and the other trial within two divisions of Kent Police Department (United Kingdom).
Abstract: The concentration of police resources in stable crime hotspots has proven effective in reducing crime, but the extent to which police can disrupt dynamically changing crime hotspots is unknown. Police must be able to anticipate the future location of dynamic hotspots to disrupt them. Here we report results of two randomized controlled trials of near real-time epidemic-type aftershock sequence (ETAS) crime forecasting, one trial within three divisions of the Los Angeles Police Department and the other trial within two divisions of the Kent Police Department (United Kingdom). We investigate the extent to which (i) ETAS models of short-term crime risk outperform existing best practice of hotspot maps produced by dedicated crime analysts, (ii) police officers in the field can dynamically patrol predicted hotspots given limited resources, and (iii) crime can be reduced by predictive policing algorithms under realistic law enforcement resource constraints. While previous hotspot policing experiments fix treatme...

238 citations


Journal ArticleDOI
TL;DR: Two new statistical learning methods for estimating the optimal DTR are introduced, termed backward outcome weighted learning (BOWL) and simultaneous outcome weightedlearning (SOWL), and it is proved that the resulting rules are consistent, and provide finite sample bounds for the errors using the estimated rules.
Abstract: Dynamic treatment regimes (DTRs) are sequential decision rules for individual patients that can adapt over time to an evolving illness. The goal is to accommodate heterogeneity among patients and find the DTR which will produce the best long-term outcome if implemented. We introduce two new statistical learning methods for estimating the optimal DTR, termed backward outcome weighted learning (BOWL), and simultaneous outcome weighted learning (SOWL). These approaches convert individualized treatment selection into an either sequential or simultaneous classification problem, and can thus be applied by modifying existing machine learning techniques. The proposed methods are based on directly maximizing over all DTRs a nonparametric estimator of the expected long-term outcome; this is fundamentally different than regression-based methods, for example, Q-learning, which indirectly attempt such maximization and rely heavily on the correctness of postulated regression models. We prove that the resulting rules ar...

233 citations


Journal ArticleDOI
TL;DR: The practical applicability is enhanced through the introduction of a novel functional final prediction error model selection criterion that allows for an automatic determination of the lag structure and the dimensionality of the model.
Abstract: This article addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical tractability and the current lack of advanced functional time series methodology. It is shown here how standard multivariate prediction techniques can be used in this context. The connection between functional and multivariate predictions is made precise for the important case of vector and functional autoregressions. The proposed method is easy to implement, making use of existing statistical software packages, and may, therefore, be attractive to a broader, possibly nonacademic, audience. Its practical applicability is enhanced through the introduction of a novel functional final prediction error model selection criterion that allows for an automatic determination of the lag structure and the dimensionality of the model. The usefulness of the proposed methodology is demonstrated in a simulation study and an application to environmental data, namely the prediction of daily pollution curves describing the concentration of particulate matter in ambient air. It is found that the proposed prediction method often significantly outperforms existing methods.

220 citations


Journal ArticleDOI
TL;DR: In this article, a Markov chain Monte Carlo (MCMCMC) algorithm is proposed to estimate the model parameters and latent positions of the actors in the network. And a novel approach is given to detect and visualize an attracting influence between actors using only the edge information.
Abstract: Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. We propose Markov chain Monte Carlo (MCMC) algorithm to estimate the model parameters and latent positions of the actors in the network. The model yields meaningful visualization of dynamic networks, giving the researcher insight into the evolution and the structure, both local and global, of the network. The model handles directed or undirected edges, easily handles missing edges, and lends itself well to predicting future edges. Further, a novel approach is given to detect and visualize an attracting influence between actors using only the edge information. We use the case-control likelihood approximation to speed up the estimation algorithm, modifying it slightly to account for missing data. We apply the latent space model to data collected from a Dutch classroom, and a cosp...

207 citations


Journal ArticleDOI
TL;DR: A marginal feature screening procedure based on empirical conditional distribution function is proposed that is model-free in that its implementation does not require specification of a regression model and robust to heavy-tailed distributions of predictors and the presence of potential outliers.
Abstract: This work is concerned with marginal sure independence feature screening for ultrahigh dimensional discriminant analysis. The response variable is categorical in discriminant analysis. This enables us to use the conditional distribution function to construct a new index for feature screening. In this article, we propose a marginal feature screening procedure based on empirical conditional distribution function. We establish the sure screening and ranking consistency properties for the proposed procedure without assuming any moment condition on the predictors. The proposed procedure enjoys several appealing merits. First, it is model-free in that its implementation does not require specification of a regression model. Second, it is robust to heavy-tailed distributions of predictors and the presence of potential outliers. Third, it allows the categorical response having a diverging number of classes in the order of O(nκ) with some κ ⩾ 0. We assess the finite sample property of the proposed procedure by Mont...

194 citations


Journal ArticleDOI
TL;DR: In this paper, a regression discontinuity (RD) identification and estimation away from the cutoff is discussed, where the identification strategy exploits the availability of dependent variable predictors other than the running variable.
Abstract: In regression discontinuity (RD) studies exploiting an award or admissions cutoff, causal effects are nonparametrically identified for those near the cutoff. The effect of treatment on inframarginal applicants is also of interest, but identification of such effects requires stronger assumptions than those required for identification at the cutoff. This article discusses RD identification and estimation away from the cutoff. Our identification strategy exploits the availability of dependent variable predictors other than the running variable. Conditional on these predictors, the running variable is assumed to be ignorable. This identification strategy is used to study effects of Boston exam schools for inframarginal applicants. Identification based on the conditional independence assumptions imposed in our framework yields reasonably precise and surprisingly robust estimates of the effects of exam school attendance on inframarginal applicants. These estimates suggest that the causal effects of exam school ...

191 citations


Journal ArticleDOI
TL;DR: This article addresses the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features, and proposes a Bayesian approach to inference on multiple Gaussian graphical models.
Abstract: In this article, we propose a Bayesian approach to inference on multiple Gaussian graphical models. Specifically, we address the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features. We link the estimation of the graph structures via a Markov random field (MRF) prior, which encourages common edges. We learn which sample groups have a shared graph structure by placing a spike-and-slab prior on the parameters that measure network relatedness. This approach allows us to share information between sample groups, when appropriate, as well as to obtain a measure of relative network similarity across groups. Our modeling framework incorporates relevant prior knowledge through an edge-specific informative prior and can encourage similarity to an established network. Through simulations, we demonstrate the utility of our method in summarizing relative network similarity and compare its performance against related methods. We ...

189 citations


Journal ArticleDOI
TL;DR: A new type of tree-based method, reinforcement learning trees (RLT), which exhibits significantly improved performance over traditional methods such as random forests under high-dimensional settings and a variable muting procedure that progressively eliminates noise variables during the construction of each individual tree.
Abstract: In this paper, we introduce a new type of tree-based method, reinforcement learning trees (RLT), which exhibits significantly improved performance over traditional methods such as random forests (Breiman, 2001) under high-dimensional settings. The innovations are three-fold. First, the new method implements reinforcement learning at each selection of a splitting variable during the tree construction processes. By splitting on the variable that brings the greatest future improvement in later splits, rather than choosing the one with largest marginal effect from the immediate split, the constructed tree utilizes the available samples in a more efficient way. Moreover, such an approach enables linear combination cuts at little extra computational cost. Second, we propose a variable muting procedure that progressively eliminates noise variables during the construction of each individual tree. The muting procedure also takes advantage of reinforcement learning and prevents noise variables from being considered in the search for splitting rules, so that towards terminal nodes, where the sample size is small, the splitting rules are still constructed from only strong variables. Last, we investigate asymptotic properties of the proposed method under basic assumptions and discuss rationale in general settings.

Journal ArticleDOI
TL;DR: Estimation procedure for the Q-matrix under the DINA and the DINO models through the regularized maximum likelihood is proposed and Simulation studies show that the proposed method admits high probability recovering the true Q-Matrix.
Abstract: Diagnostic classification models (DMCs) have recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Central to the model specification is the so-called Q-matrix that provides a qualitative specification of the item-attribute relationship. In this article, we develop theories on the identifiability for the Q-matrix under the DINA and the DINO models. We further propose an estimation procedure for the Q-matrix through the regularized maximum likelihood. The applicability of this procedure is not limited to the DINA or the DINO model and it can be applied to essentially all Q-matrix based DMCs. Simulation studies show that the proposed method admits high probability recovering the true Q-matrix. Furthermore, two case studies are presented. The first case is a dataset on fraction subtraction (educational application) and the second case is a subsample of the National Epidemiological Survey on Alcohol and Related Conditions concerning the social anxiety disord...

Journal ArticleDOI
TL;DR: In this article, the authors propose a generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators.
Abstract: Over the past decade, doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models. These are asymptotically unbiased when at least one of two nuisance working models is correctly specified, regardless of which. While their asymptotic distribution is not affected by the choice of root-n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified, this choice of estimators can have a dramatic impact under misspecification of at least one working model. In this article, we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models, which is designed to improve the performance of the doubly robust estimator of interest, relative to the default use of maximum likelihood estimators for the nuisance parameters. The proposed approach locally minimizes the squared first-order asymptotic bias of the doubly robust estim...

Journal ArticleDOI
TL;DR: In this paper, a general class of Bayesian generalized additive models for zero-inflated and overdispersed count data was proposed for location, scale, and shape where semiparametric predictors can be specified for several parameters of a count data distribution.
Abstract: Frequent problems in applied research preventing the application of the classical Poisson log-linear model for analyzing count data include overdispersion, an excess of zeros compared to the Poisson distribution, correlated responses, as well as complex predictor structures comprising nonlinear effects of continuous covariates, interactions or spatial effects. We propose a general class of Bayesian generalized additive models for zero-inflated and overdispersed count data within the framework of generalized additive models for location, scale, and shape where semiparametric predictors can be specified for several parameters of a count data distribution. As standard options for applied work we consider the zero-inflated Poisson, the negative binomial and the zero-inflated negative binomial distribution. The additive predictor specifications rely on basis function approximations for the different types of effects in combination with Gaussian smoothness priors. We develop Bayesian inference based on Markov c...

Journal ArticleDOI
TL;DR: This article reviews standard designs available to applied researchers, develops various multivariate regression techniques for substantive analyses, proposes power analyses to help improve research designs, and presents new robust designs that are based on less stringent assumptions than those of the standard designs.
Abstract: About a half century ago, in 1965, Warner proposed the randomized response method as a survey technique to reduce potential bias due to nonresponse and social desirability when asking questions about sensitive behaviors and beliefs. This method asks respondents to use a randomization device, such as a coin flip, whose outcome is unobserved by the interviewer. By introducing random noise, the method conceals individual responses and protects respondent privacy. While numerous methodological advances have been made, we find surprisingly few applications of this promising survey technique. In this article, we address this gap by (1) reviewing standard designs available to applied researchers, (2) developing various multivariate regression techniques for substantive analyses, (3) proposing power analyses to help improve research designs, (4) presenting new robust designs that are based on less stringent assumptions than those of the standard designs, and (5) making all described methods available through open...

Journal ArticleDOI
TL;DR: In this paper, a posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors, and then selects a subset of variables for linear models.
Abstract: Selecting a subset of variables for linear models remains an active area of research. This article reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors.

Journal ArticleDOI
TL;DR: In this paper, a nonparametric test for the population mean vector of non-normal high-dimensional multivariate data was proposed, and the authors proved that the limiting null distribution of the proposed test is normal under mild conditions.
Abstract: This work is concerned with testing the population mean vector of nonnormal high-dimensional multivariate data. Several tests for high-dimensional mean vector, based on modifying the classical Hotelling T2 test, have been proposed in the literature. Despite their usefulness, they tend to have unsatisfactory power performance for heavy-tailed multivariate data, which frequently arise in genomics and quantitative finance. This article proposes a novel high-dimensional nonparametric test for the population mean vector for a general class of multivariate distributions. With the aid of new tools in modern probability theory, we proved that the limiting null distribution of the proposed test is normal under mild conditions when p is substantially larger than n. We further study the local power of the proposed test and compare its relative efficiency with a modified Hotelling T2 test for high-dimensional data. An interesting finding is that the newly proposed test can have even more substantial power gain with l...

Journal ArticleDOI
TL;DR: Through the analysis of a dataset of ultra high frequency order book updates, this work introduces a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data and uses a stochastic mechanism to switch from one period of constant reference price to another.
Abstract: Through the analysis of a dataset of ultra high frequency order book updates, we introduce a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data. To do so, we split the time interval of interest into periods in which a well chosen reference price, typically the midprice, remains constant. Within these periods, we view the limit order book as a Markov queuing system. Indeed, we assume that the intensities of the order flows only depend on the current state of the order book. We establish the limiting behavior of this model and estimate its parameters from market data. Then, to design a relevant model for the whole period of interest, we use a stochastic mechanism that allows to switch from one period of constant reference price to another. Beyond enabling to reproduce accurately the behavior of market data, we show that our framework can be very useful for practitioners, notably as a market simulator or as a tool for th...

Journal ArticleDOI
Juan Shen1, Xuming He
TL;DR: In this article, the authors proposed a statistical model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership.
Abstract: In this article, we propose a statistical model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership. The need for such subgroup identification arises in clinical trials and in market segmentation analysis. By using a structured logistic-normal mixture model, our proposed framework enables us to perform a confirmatory statistical test for the existence of subgroups, and at the same time, to construct predictive scores for the subgroup membership. The inferential procedure proposed in the article is built on the recent literature on hypothesis testing for Gaussian mixtures, but the structured logistic-normal mixture model enjoys some distinctive properties that are unavailable to the simpler Gaussian mixture models. With the bootstrap approximations, the proposed tests are shown to be powerful and, equally importantly, insensitive to the choice of tuning parameters. As an illustration, we analyze a dataset fr...

Journal ArticleDOI
TL;DR: A nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions that is proven to be more powerful than some recently developed tests through the authors' numerical simulations and able to identify two conditionally associated gene expressions, which otherwise cannot be revealed.
Abstract: Statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models. The classic measures focus on linear conditional correlations, and are incapable of characterizing non-linear conditional relationship including non-monotonic relationship. To overcome this limitation, we introduces a nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions. Our measure possesses the necessary and intuitive properties as a correlation index. Briefly, it is zero almost surely if and only if two multivariate random variables are conditionally independent given a third random variable. More importantly, the sample version of this measure can be expressed elegantly as the root of a V or U-process with random kernels and has desirable theoretical properties. Based on the sample version, we propose a test for conditional independence, which is proven to be more powerful than some recently developed tests through our numerical simulations. The advantage of our test is even greater when the relationship between the multivariate random variables given the third random variable cannot be expressed in a linear or monotonic function of one random variable versus the other. We also show that the sample measure is consistent and weakly convergent, and the test statistic is asymptotically normal. By applying our test in a real data analysis, we are able to identify two conditionally associated gene expressions, which otherwise cannot be revealed. Thus, our measure of conditional dependence is not only an ideal concept, but also has important practical utility.

Journal ArticleDOI
TL;DR: In this article, the authors consider identifiability and estimation in a generalized linear model in which the response variable and some covariates have missing values and the missing data mechanism is nonignorable and unspecified.
Abstract: We consider identifiability and estimation in a generalized linear model in which the response variable and some covariates have missing values and the missing data mechanism is nonignorable and unspecified. We adopt a pseudo-likelihood approach that makes use of an instrumental variable to help identifying unknown parameters in the presence of nonignorable missing data. Explicit conditions for the identifiability of parameters are given. Some asymptotic properties of the parameter estimators based on maximizing the pseudo-likelihood are established. Explicit asymptotic covariance matrix and its estimator are also derived in some cases. For the numerical maximization of the pseudo-likelihood, we develop a two-step iteration algorithm that decomposes a nonconcave maximization problem into two problems of maximizing concave functions. Some simulation results and an application to a dataset from cotton factory workers are also presented.

Journal ArticleDOI
TL;DR: A new form of matching is introduced that matches patients of each new surgeon to patients of an otherwise similar experienced surgeon at the same hospital, perfectly balancing 176 surgical procedures and closely balancing a total of 2.9 million categories of patients.
Abstract: Every newly trained surgeon performs her first unsupervised operation. How do the health outcomes of her patients compare with the patients of experienced surgeons? Using data from 498 hospitals, we compare 1252 pairs comprised of a new surgeon and an experienced surgeon working at the same hospital. We introduce a new form of matching that matches patients of each new surgeon to patients of an otherwise similar experienced surgeon at the same hospital, perfectly balancing 176 surgical procedures and closely balancing a total of 2.9 million categories of patients; additionally, the individual patient pairs are as close as possible. A new goal for matching is introduced, called "refined covariate balance," in which a sequence of nested, ever more refined, nominal covariates is balanced as closely as possible, emphasizing the first or coarsest covariate in that sequence. A new algorithm for matching is proposed and the main new results prove that the algorithm finds the closest match in terms of the total within-pair covariate distances among all matches that achieve refined covariate balance. Unlike previous approaches to forcing balance on covariates, the new algorithm creates multiple paths to a match in a network, where paths that introduce imbalances are penalized and hence avoided to the extent possible. The algorithm exploits a sparse network to quickly optimize a match that is about two orders of magnitude larger than is typical in statistical matching problems, thereby permitting much more extensive use of fine and near-fine balance constraints. The match was constructed in a few minutes using a network optimization algorithm implemented in R. An R package called rcbalance implementing the method is available from CRAN.

Journal ArticleDOI
TL;DR: In this article, quantile autocorrelation function (QACF) and quantile partial correlation (QPACF) were proposed to identify the autoregressive order of a model.
Abstract: In this article, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the Box–Jenkins three-stage procedure (model identification, model parameter estimation, and model diagnostic checking) from classical autoregressive models to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the fitted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR and QPCOR, but also show the large sample results of QACF, QPACF, and the quantile version of the Box–Pierce test. Moreover, we obtain the bootstrap approximations to the distributions of parameter estimators and p...

Journal ArticleDOI
TL;DR: In this paper, the authors provide a detailed discussion about the use of self-normalization in different contexts and highlight distinctive feature associated with each problem and connections among these recent developments.
Abstract: This article reviews some recent developments on the inference of time series data using the self-normalized approach. We aim to provide a detailed discussion about the use of self-normalization in different contexts and highlight distinctive feature associated with each problem and connections among these recent developments. The topics covered include: confidence interval construction for a parameter in a weakly dependent stationary time series setting, change point detection in the mean, robust inference in regression models with weakly dependent errors, inference for nonparametric time series regression, inference for long memory time series, locally stationary time series and near-integrated time series, change point detection, and two-sample inference for functional time series, as well as the use of self-normalization for spatial data and spatial-temporal data. Some new variations of the self-normalized approach are also introduced with additional simulation results. We also provide a brief review ...

Journal ArticleDOI
TL;DR: In this paper, the authors extend the class of score type change point statistics considered in 2007 by Huskova, Praskova, and Steinebach to the vector autoregressive (VAR) case and the epidemic change alternative.
Abstract: The primary contributions of this article are rigorously developed novel statistical methods for detecting change points in multivariate time series. We extend the class of score type change point statistics considered in 2007 by Huskova, Praskova, and Steinebach to the vector autoregressive (VAR) case and the epidemic change alternative. Our proposed procedures do not require the observed time series to actually follow the VAR model. Instead, following the strategy implicitly employed by practitioners, our approach takes model misspecification into account so that our detection procedure uses the model background merely for feature extraction. We derive the asymptotic distributions of our test statistics and show that our procedure has asymptotic power of 1. The proposed test statistics require the estimation of the inverse of the long-run covariance matrix which is particularly difficult in higher-dimensional settings (i.e., where the dimension of the time series and the dimension of the parameter vecto...

Journal ArticleDOI
TL;DR: A meta-analysis for heterogeneous studies is introduced by combining the confidence density functions derived from the summary statistics of individual studies, hence referred to as the CD approach, which obtains a unifying approach for combining summary statistics, subsuming many of the existingMeta-analysis methods as special cases.
Abstract: Meta-analysis has been widely used to synthesize evidence from multiple studies for common hypotheses or parameters of interest. However, it has not yet been fully developed for incorporating heterogeneous studies, which arise often in applications due to different study designs, populations, or outcomes. For heterogeneous studies, the parameter of interest may not be estimable for certain studies, and in such a case, these studies are typically excluded from conventional meta-analysis. The exclusion of part of the studies can lead to a nonnegligible loss of information. This article introduces a meta-analysis for heterogeneous studies by combining the confidence density functions derived from the summary statistics of individual studies, hence referred to as the CD approach. It includes all the studies in the analysis and makes use of all information, direct as well as indirect. Under a general likelihood inference framework, this new approach is shown to have several desirable properties, including: (i)...

Journal ArticleDOI
TL;DR: In this paper, the covariate balancing propensity score (CBPS) methodology is generalized to longitudinal analysis settings, which incorporates all covariate balance conditions across multiple time periods, and the CBPS estimates the inverse probability weights such that the resulting covariate imbalance is improved.
Abstract: Marginal structural models (MSMs) are becoming increasingly popular as a tool for causal inference from longitudinal data. Unlike standard regression models, MSMs can adjust for time-dependent observed confounders while avoiding the bias due to the direct adjustment for covariates affected by the treatment. Despite their theoretical appeal, a main practical difficulty of MSMs is the required estimation of inverse probability weights. Previous studies have found that MSMs can be highly sensitive to misspecification of treatment assignment model even when the number of time periods is moderate. To address this problem, we generalize the covariate balancing propensity score (CBPS) methodology of Imai and Ratkovic to longitudinal analysis settings. The CBPS estimates the inverse probability weights such that the resulting covariate balance is improved. Unlike the standard approach, the proposed methodology incorporates all covariate balancing conditions across multiple time periods. Since the number of these ...

Journal ArticleDOI
TL;DR: In this article, a nonparametric procedure is proposed for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process.
Abstract: We propose a new nonparametric procedure (referred to as MuBreD) for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (second-order) piecewise stationary process, which also identifies the components of the series where the breaks occur. MuBreD is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows us to prove the existence of structural breaks at a controlled Type I error. Second, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point, and addresses the problem of m...

Journal ArticleDOI
TL;DR: In this article, the problem of estimating in a quantile regression model when observations are missing at random under independent and non-identically distributed errors is examined. And three approaches of handling this problem based on nonparametric inverse probability weighting, estimating equations projection, and a combination of both are presented.
Abstract: This article examines the problem of estimation in a quantile regression model when observations are missing at random under independent and nonidentically distributed errors. We consider three approaches of handling this problem based on nonparametric inverse probability weighting, estimating equations projection, and a combination of both. An important distinguishing feature of our methods is their ability to handle missing response and/or partially missing covariates, whereas existing techniques can handle only one or the other, but not both. We prove that our methods yield asymptotically equivalent estimators that achieve the desirable asymptotic properties of unbiasedness, normality, and n-consistency. Because we do not assume that the errors are identically distributed, our theoretical results are valid under heteroscedasticity, a particularly strong feature of our methods. Under the special case of identical error distributions, all of our proposed estimators achieve the semiparametric efficiency b...

Journal ArticleDOI
TL;DR: A test statistic for testing the equality of two population mean vectors in the “large-p-small-n” setting is developed, which is robust to heteroscedasticity in the component variances, and requires very little computation time, which allows its use in settings with very large p.
Abstract: We develop a test statistic for testing the equality of two population mean vectors in the “large-p-small-n” setting. Such a test must surmount the rank-deficiency of the sample covariance matrix, which breaks down the classic Hotelling T2 test. The proposed procedure, called the generalized component test, avoids full estimation of the covariance matrix by assuming that the p components admit a logical ordering such that the dependence between components is related to their displacement. The test is shown to be competitive with other recently developed methods under ARMA and long-range dependence structures and to achieve superior power for heavy-tailed data. The test does not assume equality of covariance matrices between the two populations, is robust to heteroscedasticity in the component variances, and requires very little computation time, which allows its use in settings with very large p. An analysis of mitochondrial calcium concentration in mouse cardiac muscles over time and of copy number varia...