Showing papers in "Biometrika in 2017"
TL;DR: This work applies the clustering method to large brain graphs derived from diffusion MRI data, using the node locations or neurological region membership as covariates, and yields results superior both to regularized spectral clustering without node covariates and to an adaptation of canonical correlation analysis.
Abstract: Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides insight into the systems that generated the graphs. Moreover, in applications such as connectomics, social networks, and genomics, graph data are accompanied by contextualizing measures on each node. We utilize these node covariates to help uncover latent communities in a graph, using a modification of spectral clustering. Statistical guarantees are provided under a joint mixture model that we call the node-contextualized stochastic blockmodel, including a bound on the misclustering rate. The bound is used to derive conditions for achieving perfect clustering. For most simulated cases, covariate-assisted spectral clustering yields results superior both to regularized spectral clustering without node covariates and to an adaptation of canonical correlation analysis. We apply our clustering method to large brain graphs derived from diffusion MRI data, using the node locations or neurological region membership as covariates. In both cases, covariate-assisted spectral clustering yields clusters that are easier to interpret neurologically.
138 citations
TL;DR: It is found that while targeted minimum loss‐based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose.
Abstract: Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.
116 citations
Abstract: SummaryBayesian robustness under model misspecification is a current area of active research. Among recent ideas is that of raising the likelihood function to a power. In this paper we discuss the choice of appropriate power and provide examples.
96 citations
TL;DR: In this article, a neighbourhood smoothing method is proposed to estimate the expectation of the adjacency matrix directly without making the structural assumptions that graphon estimation requires, which has a competitive mean squared error rate and outperforms many benchmark methods for link prediction.
Abstract: SummaryThe estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighbourhood smoothing method requires little tuning, has a competitive mean squared error rate and outperforms many benchmark methods for link prediction in simulated and real networks.
74 citations
TL;DR: Monte Carlo simulation studies indicate that the projection correlation has higher power than the distance correlation and the ranks of distances in tests of independence, especially when the dimensions are relatively large or the moment conditions required by thedistance correlation are violated.
Abstract: We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We show that the sample estimate of the projection correction is [Formula: see text]-consistent if the two random vectors are independent and root-[Formula: see text]-consistent otherwise. Monte Carlo simulation studies indicate that the projection correlation has higher power than the distance correlation and the ranks of distances in tests of independence, especially when the dimensions are relatively large or the moment conditions required by the distance correlation are violated.
69 citations
TL;DR: This work proposes a simple and general posterior interval estimation algorithm to rapidly and accurately estimate quantiles of the posterior distributions for one‐dimensional functionals and has a better balance of accuracy and efficiency than its competitors across a variety of simulations and a real‐data example.
Abstract: SummaryStandard posterior sampling algorithms, such as Markov chain Monte Carlo procedures, face major challenges in scaling up to massive datasets. We propose a simple and general posterior interval estimation algorithm to rapidly and accurately estimate quantiles of the posterior distributions for one-dimensional functionals. Our algorithm runs Markov chain Monte Carlo in parallel for subsets of the data, and then averages quantiles estimated from each subset. We provide strong theoretical guarantees and show that the credible intervals from our algorithm asymptotically approximate those from the full posterior in the leading parametric order. Our algorithm has a better balance of accuracy and efficiency than its competitors across a variety of simulations and a real-data example.
55 citations
TL;DR: In this paper, the authors introduce multiply robust imputation in finite population sampling, which is closely related to multiple robustness, which extends double robustness and is shown to have low bias and high efficiency.
Abstract: SummaryItem nonresponse in surveys is often treated through some form of imputation. We introduce multiply robust imputation in finite population sampling. This is closely related to multiple robustness, which extends double robustness. In practice, multiple nonresponse models and multiple imputation models may be fitted, each involving different subsets of covariates and possibly different link functions. An imputation procedure is said to be multiply robust if the resulting estimator is consistent when all models but one are misspecified. A jackknife variance estimator is proposed and shown to be consistent. Random and fractional imputation procedures are discussed. A simulation study suggests that the proposed estimation procedures have low bias and high efficiency.
55 citations
TL;DR: In this paper, a loss function called the D-trace loss is proposed to directly estimate the precision matrix difference without attempting to estimate the matrix themselves, which can yield consistent estimators in high-dimensional settings if the difference network is sparse.
Abstract: SummaryBiological networks often change under different environmental and genetic conditions. In this paper, we model network change as the difference of two precision matrices and propose a novel loss function called the D-trace loss, which allows us to directly estimate the precision matrix difference without attempting to estimate the precision matrices themselves. Under a new irrepresentability condition, we show that the D-trace loss function with the lasso penalty can yield consistent estimators in high-dimensional settings if the difference network is sparse. A very efficient algorithm is developed based on the alternating direction method of multipliers to minimize the penalized loss function. Simulation studies and a real-data analysis show that the proposed method outperforms other methods.
50 citations
TL;DR: In this paper, a new estimator of the regression causal effect inspired by minimum average variance estimation is proposed, which can be used to estimate the average causal effect, for which it is shown to be asymptotically super-efficient.
Abstract: SUMMARY In many causal inference problems the parameter of interest is the regression causal effect, defined as the conditional mean difference in the potential outcomes given covariates. In this paper we discuss how sufficient dimension reduction can be used to aid causal inference, and we propose a new estimator of the regression causal effect inspired by minimum average variance estimation. The estimator requires a weaker common support condition than propensity score-based approaches, and can be used to estimate the average causal effect, for which it is shown to be asymptotically super-efficient. Its finite-sample properties are illustrated by simulation.
46 citations
TL;DR: In this article, the authors consider the testing of mutual independence among all entries in a [formula: see text]-dimensional random vector based on independent observations and show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions.
Abstract: We consider the testing of mutual independence among all entries in a [Formula: see text]-dimensional random vector based on [Formula: see text] independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and Spearman's rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where [Formula: see text]. We further show that the two tests are rate-optimal in terms of power against sparse alternatives and that they outperform competitors in simulations, especially when [Formula: see text] is large.
44 citations
TL;DR: In this paper, the authors proposed a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross-correlations of the component series, based on an approximation by the L∞-norm of a normal random vector, which can be evaluated by bootstrapping from a multivariate normal distribution.
Abstract: We propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross-correlations of the component series. Based on an approximation by the L∞-norm of a normal random vector, the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution. In contrast to the conventional white noise test, the new method is proved to be valid for testing departure from white noise that is not independent and identically distributed. We illustrate the accuracy and the power of the proposed test by simulation, which also shows that the new test outperforms several commonly used methods, including the Lagrange multiplier test and the multivariate Box–Pierce portmanteau tests, especially when the dimension of the time series is high in relation to the sample size. The numerical results also indicate that the performance of the new test can be further enhanced when it is applied to pre-transformed data obtained via the time series principal component analysis proposed by J. Chang, B. Guo and Q. Yao (arXiv:1410.2323). The proposed procedures have been implemented in an R package.
TL;DR: The G-squared measure as discussed by the authors is a measure to test whether two univariate random variables are independent and to measure the strength of their relationship, which is almost identical to the square of the Pearson correlation coefficient.
Abstract: Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation coefficient is effective for capturing linear dependence, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns. We introduce a new measure, G-squared, to test whether two univariate random variables are independent and to measure the strength of their relationship. The G-squared statistic is almost identical to the square of the Pearson correlation coefficient, R-squared, for linear relationships with constant error variance, and has the intuitive meaning of the piecewise R-squared between the variables. It is particularly effective in handling nonlinearity and heteroscedastic errors. We propose two estimators of G-squared and show their consistency. Simulations demonstrate that G-squared estimators are among the most powerful test statistics compared with several state-of-the-art methods.
TL;DR: It is shown that the proposed estimators for the finite‐dimensional parameters are consistent and asymptotically normal, with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood.
Abstract: Interval-censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval. We investigate the effects of possibly time-dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects, and we study nonparametric maximum likelihood estimation under general interval-censoring schemes. We show that the proposed estimators for the finite-dimensional parameters are consistent and asymptotically normal, with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood. In addition, we develop an EM algorithm that converges stably for arbitrary datasets. Finally, we assess the performance of the proposed methods in extensive simulation studies and illustrate their application using data derived from the Atherosclerosis Risk in Communities Study.
TL;DR: In this article, a robust reduced-rank regression approach for joint modeling and outlier detection is proposed, which is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods.
Abstract: In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint modelling and outlier detection. The problem is formulated as a regularized multivariate regression with a sparse mean-shift parameterization, which generalizes and unifies some popular robust multivariate methods. An efficient thresholding-based iterative procedure is developed for optimization. We show that the algorithm is guaranteed to converge and that the coordinatewise minimum point produced is statistically accurate under regularity conditions. Our theoretical investigations focus on non-asymptotic robust analysis, demonstrating that joint rank reduction and outlier detection leads to improved prediction accuracy. In particular, we show that redescending [Formula: see text]-functions can essentially attain the minimax optimal error rate, and in some less challenging problems convex regularization guarantees the same low error rate. The performance of the proposed method is examined through simulation studies and real-data examples.
TL;DR: This paper showed that when the treatment follows an additive or multiplicative model conditional on the instrumental variable and the confounder, these monotonicity assumptions can be interpreted as the signs of the arrows of the causal diagrams.
Abstract: Drawing causal inference with observational studies is the central pillar of many disciplines. One sufficient condition for identifying the causal effect is that the treatment-outcome relationship is unconfounded conditional on the observed covariates. It is often believed that the more covariates we condition on, the more plausible this unconfoundedness assumption is. This belief has had a huge impact on practical causal inference, suggesting that we should adjust for all pretreatment covariates. However, when there is unmeasured confounding between the treatment and outcome, estimators adjusting for some pretreatment covariate might have greater bias than estimators without adjusting for this covariate. This kind of covariate is called a bias amplifier, and includes instrumental variables that are independent of the confounder, and affect the outcome only through the treatment. Previously, theoretical results for this phenomenon have been established only for linear models. We fill in this gap in the literature by providing a general theory, showing that this phenomenon happens under a wide class of models satisfying certain monotonicity assumptions. We further show that when the treatment follows an additive or multiplicative model conditional on the instrumental variable and the confounder, these monotonicity assumptions can be interpreted as the signs of the arrows of the causal diagrams.
TL;DR: In this article, the authors considered the Pitman-Yor process with an atom in its base measure and derived computable expressions for the distribution of induced random partitions and for the predictive distributions.
Abstract: SummaryFor the most popular discrete nonparametric models, beyond the Dirichlet process, the prior guess at the shape of the data-generating distribution, also known as the base measure, is assumed to be diffuse. Such a specification greatly simplifies the derivation of analytical results, allowing for a straightforward implementation of Bayesian nonparametric inferential procedures. However, in several applied problems the available prior information leads naturally to the incorporation of an atom into the base measure, and then the Dirichlet process is essentially the only tractable choice for the prior. In this paper we fill this gap by considering the Pitman–Yor process with an atom in its base measure. We derive computable expressions for the distribution of the induced random partitions and for the predictive distributions. These findings allow us to devise an effective generalized Polya urn Gibbs sampler. Applications to density estimation, clustering and curve estimation, with both simulated and real data, serve as an illustration of our results and allow comparisons with existing methodology. In particular, we tackle a functional data analysis problem concerning basal body temperature curves.
TL;DR: In this paper, a substitution variable is proposed to use in place of the latent membership in the always-survivor group to identify and estimate the average causal effect among the subgroup consisting of subjects who would survive under either exposure.
Abstract: It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis.
TL;DR: The proposed classifiers can be viewed as an extension to functional data of some of the earliest nonparametric Bayes classifiers that were based on simple density ratios in the one‐dimensional case.
Abstract: Bayes classifiers for functional data pose a challenge. This is because probability
density functions do not exist for functional data. As a consequence, the classical Bayes
classifier using density quotients needs to be modified. We propose to use density ratios
of projections on a sequence of eigenfunctions that are common to the groups to be
classified. The density ratios can then be factored into density ratios of individual
functional principal components whence the classification problem is reduced to a sequence
of nonparametric one-dimensional density estimates. This is an extension to functional data
of some of the very earliest nonparametric Bayes classifiers that were based on simple
density ratios in the one-dimensional case. By means of the factorization of the density
quotients the curse of dimensionality that would otherwise severely affect Bayes
classifiers for functional data can be avoided. We demonstrate that in the case of Gaussian
functional data, the proposed functional Bayes classifier reduces to a functional version
of the classical quadratic discriminant. A study of the asymptotic behavior of the proposed
classifiers in the large sample limit shows that under certain conditions the
misclassification rate converges to zero, a phenomenon that has been referred to as
"perfect classification". The proposed classifiers also perform favorably in finite sample
applications, as we demonstrate in comparisons with other functional classifiers in
simulations and various data applications, including wine spectral data, functional
magnetic resonance imaging (fMRI) data for attention deficit hyperactivity disorder (ADHD)
patients, and yeast gene expression data.
TL;DR: In this article, a local principal component analysis approach is proposed to estimate the number of common factors of a continuous-time factor model with time-varying factor loadings using high frequency data.
Abstract: SummaryIn this paper, we introduce a local principal component analysis approach to determining the number of common factors of a continuous-time factor model with time-varying factor loadings using high-frequency data. The model is approximated locally on shrinking blocks using discrete-time factor models. The number of common factors is estimated by minimizing the penalized aggregated mean squared residual error over all shrinking blocks. While the local mean squared residual error on each block converges at rate $\min(n^{1/4}, p)$, where $n$ is the sample size and $p$ is the dimension, the aggregated mean squared residual error converges at rate $\min(n^{1/2}, p)$; this achieves the convergence rate of the penalized criterion function of the global principal component analysis method, assuming restrictive constant factor loading. An estimator of the number of factors based on the local principal component analysis is consistent. Simulation results justify the performance of our estimator. A real financial dataset is analysed.
TL;DR: In this paper, the authors thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the Monte Carlo Inference for Complex Statistical Models when work on this paper was undertaken.
Abstract: The authors thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme Monte Carlo Inference for Complex Statistical Models when work on this paper was undertaken. This work was supported by the Engineering and Physical Sciences Research Council [grant numbers EP/K020153/1, EP/K032208/1] and the Swedish Research Council [contract number 2016-04278].
TL;DR: In this paper, a geometric object for tree space similar to the [Formula: see text]th principal component in Euclidean space: the locus of the weighted Frechet mean of vertex trees when the weights vary over the complex.
Abstract: Evolutionary relationships are represented by phylogenetic trees, and a phylogenetic analysis of gene sequences typically produces a collection of these trees, one for each gene in the analysis. Analysis of samples of trees is difficult due to the multi-dimensionality of the space of possible trees. In Euclidean spaces, principal component analysis is a popular method of reducing high-dimensional data to a low-dimensional representation that preserves much of the sample's structure. However, the space of all phylogenetic trees on a fixed set of species does not form a Euclidean vector space, and methods adapted to tree space are needed. Previous work introduced the notion of a principal geodesic in this space, analogous to the first principal component. Here we propose a geometric object for tree space similar to the [Formula: see text]th principal component in Euclidean space: the locus of the weighted Frechet mean of [Formula: see text] vertex trees when the weights vary over the [Formula: see text]-simplex. We establish some basic properties of these objects, in particular showing that they have dimension [Formula: see text], and propose algorithms for projection onto these surfaces and for finding the principal locus associated with a sample of trees. Simulation studies demonstrate that these algorithms perform well, and analyses of two datasets, containing Apicomplexa and African coelacanth genomes respectively, reveal important structure from the second principal components.
TL;DR: This work investigates general structures conducive to the construction of so‐called multiply robust estimating functions, whose computation requires postulating several dimension‐reducing models but which have mean zero at the true parameter value provided one of these models is correct.
Abstract: We consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation-independent factors. We are interested in a finite-dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions. We investigate general structures conducive to the construction of so-called multiply robust estimating functions, whose computation requires postulating several dimension-reducing models but which have mean zero at the true parameter value provided one of these models is correct.
TL;DR: For regular parametric problems, this paper showed how median centring of the maximum likelihood estimate can be achieved by a simple modification of the score equation, which does not require finiteness of the estimation and is effective in preventing infinite estimates.
Abstract: For regular parametric problems, we show how median centring of the maximum likelihood estimate can be achieved by a simple modification of the score equation. For a scalar parameter of interest, the estimator is equivariant under interest-respecting reparameterizations and is third-order median unbiased. With a vector parameter of interest, componentwise equivariance and third-order median centring are obtained. Like the implicit method of Firth (1993) for bias reduction, the new method does not require finiteness of the maximum likelihood estimate and is effective in preventing infinite estimates. Simulation results for continuous and discrete models, including binary and beta regression, confirm that the method succeeds in achieving componentwise median centring and in solving the boundary estimate problem, while keeping comparable dispersion and the same approximate distribution as its main competitors.
TL;DR: In this article, a functional extension of the Monte Carlo likelihood method of Mitchell et al. (2006) and two quadratic forms based on asymptotic distributions of maximum likelihood estimators are presented.
Abstract: SummarySeparability is a common simplifying assumption on the covariance structure of spatiotemporal functional data. We present three tests of separability, one a functional extension of the Monte Carlo likelihood method of Mitchell et al. (2006) and two based on quadratic forms. Our tests are based on asymptotic distributions of maximum likelihood estimators and do not require Monte Carlo simulation. The main theoretical contribution of this paper is the specification of the joint asymptotic distribution of these estimators, which can be used to derive many other tests. The main methodological finding is that one of the quadratic form methods, which we call a norm approach, emerges as a clear winner in terms of finite-sample performance in nearly every setting we considered. This approach focuses directly on the Frobenius distance between the spatiotemporal covariance function and its separable approximation. We demonstrate the efficacy of our methods via simulations and application to Irish wind data.
TL;DR: In this paper, a nonignorable missingness mechanism for multivariate missing data is introduced, in which each study variable and its nonresponse indicator are conditionally independent given the remaining variables and their nonresponse indicators.
Abstract: SUMMARY We introduce a nonresponse mechanism for multivariate missing data in which each study variable and its nonresponse indicator are conditionally independent given the remaining variables and their nonresponse indicators. This is a nonignorable missingness mechanism, in that nonresponse for any item can depend on values of other items that are themselves missing. We show that under this itemwise conditionally independent nonresponse assumption, one can define and identify nonparametric saturated classes of joint multivariate models for the study variables and their missingness indicators. We also show how to perform sensitivity analysis with respect to violations of the conditional independence assumptions encoded by this missingness mechanism. We illustrate the proposed modelling approach with data analyses.
TL;DR: This work derives simple yet accurate approximations for Roy's test for rank‐one effects for the most common low‐dimensional settings, including signal detection in noise, multiple response regression, multivariate analysis of variance and canonical correlation analysis.
Abstract: Roy's largest root is a common test statistic in a variety of hy- pothesis testing problems. Despite its popularity, obtaining accurate tractable approximations to its distribution under the alternative has been a long- standing open problem in multivariate statistics. In this paper, assuming Gaussian observations and a rank one alternative, also known as concen- trated non-centrality, we derive simple yet accurate approximations for the distribution of Roy's largest root test for five of the most common settings. These include signal detection in noise, multivariate analysis of variance and canonical correlation analysis. Our main result is that in all five cases Roy's test can be approximated using simple combinations of standard uni- variate distributions, such as central and non-central χ2 and F. Our results allow approximate power calculations for Roy's test, as well as estimates of sample size required to detect given (rank-one) effects by this test, both of which are important quantities in hypothesis-driven research.
TL;DR: This paper proposes principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification, and its asymptotic properties are studied, and an efficient computing algorithm is proposed.
Abstract: Sufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions. However, most existing methods may work poorly for binary classification. For example, sliced inverse regression (Li, 1991) can estimate at most one direction if the response is binary. In this paper we propose principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification. Its asymptotic properties are studied, and an efficient computing algorithm is proposed. Numerical examples demonstrate its performance in binary classification.
TL;DR: In this article, the authors consider situations where the data consist of a number of responses for each individual, which may include a mix of discrete and continuous variables, and propose a pseudolikelihood information criterion.
Abstract: We consider situations where the data consist of a number of responses for each individual, which may include a mix of discrete and continuous variables. The data also include a class of predictors, where the same predictor may have different physical measurements across different experiments depending on how the predictor is measured. The goal is to select which predictors affect any of the responses, where the number of such informative predictors tends to infinity as the sample size increases. There are marginal likelihoods for each experiment; we specify a pseudolikelihood combining the marginal likelihoods, and propose a pseudolikelihood information criterion. Under regularity conditions, we establish selection consistency for this criterion with unbounded true model size. The proposed method includes a Bayesian information criterion with appropriate penalty term as a special case. Simulations indicate that data integration can dramatically improve upon using only one data source.
TL;DR: This paper presents a general method of rotation for constructing orthogonal Latin hypercubes, making the rotation idea applicable to many more situations than the original method allows.
Abstract: SummaryOrthogonal Latin hypercubes provide a class of useful designs for computer experiments. Among the available methods for constructing such designs, the method of rotation is particularly prominent due to its theoretical appeal as well as its space-filling properties. This paper presents a general method of rotation for constructing orthogonal Latin hypercubes, making the rotation idea applicable to many more situations than the original method allows. In addition to general theoretical results, many new orthogonal Latin hypercubes are obtained and tabulated.
TL;DR: Based on number theory and finite fields, three algebraic methods to construct maximin distance Latin squares as special Latin hypercube designs are proposed and lower bounds on their minimum distances are developed.
Abstract: SummaryMaximin distance Latin hypercube designs are widely used in computer experiments, yet their construction is challenging. Based on number theory and finite fields, we propose three algebraic methods to construct maximin distance Latin squares as special Latin hypercube designs. We develop lower bounds on their minimum distances. The resulting Latin squares and related Latin hypercube designs have larger minimum distances than existing ones, and are especially appealing for high-dimensional applications.