Showing papers in "Journal of the American Statistical Association in 1997"
2,526 citations
IBM1
TL;DR: In this paper, the authors present a regional L-moments algorithm for detecting homogeneous regions in a set of homogeneous data points and then select a frequency distribution for each region.
Abstract: Preface 1. Regional frequency analysis 2. L-moments 3. Screening the data 4. Identification of homogeneous regions 5. Choice of a frequency distribution 6. Estimation of the frequency distribution 7. Performance of the regional L-moment algorithm 8. Other topics 9. Examples Appendix References Index of notation.
2,329 citations
TL;DR: In this article, the authors compare several methods of estimating Bayes factors when it is possible to simulate observations from the posterior distributions, via Markov chain Monte Carlo or other techniques, provided that each posterior distribution is well behaved in the sense of having a single dominant mode.
Abstract: The Bayes factor is a ratio of two posterior normalizing constants, which may be difficult to compute. We compare several methods of estimating Bayes factors when it is possible to simulate observations from the posterior distributions, via Markov chain Monte Carlo or other techniques. The methods that we study are all easily applied without consideration of special features of the problem, provided that each posterior distribution is well behaved in the sense of having a single dominant mode. We consider a simulated version of Laplace's method, a simulated version of Bartlett correction, importance sampling, and a reciprocal importance sampling technique. We also introduce local volume corrections for each of these. In addition, we apply the bridge sampling method of Meng and Wong. We find that a simulated version of Laplace's method, with local volume correction, furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly. A simple bridge sampli...
2,191 citations
TL;DR: In this paper, the authors consider the problem of accounting for model uncertainty in linear regression models and propose two alternative approaches: the Occam's window approach and the Markov chain Monte Carlo approach.
Abstract: We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferences about quantities of interest. This approach is often not practical. In this article we offer two alternative approaches. First, we describe an ad hoc procedure, “Occam's window,” which indicates a small set of models over which a model average can be computed. Second, we describe a Markov chain Monte Carlo approach that directly approximates the exact solution. In the presence of model uncertainty, both of these model averaging procedures provide better predictive performance than any single model that might reasonably have been selected. In the extreme case where there are many candidate predictors but ...
1,804 citations
TL;DR: It is shown that a particular bootstrap method, the .632+ rule, substantially outperforms cross-validation in a catalog of 24 simulation experiments and also considers estimating the variability of an error rate estimate.
Abstract: A training set of data has been used to construct a rule for predicting future responses. What is the error rate of this rule? This is an important question both for comparing models and for assessing a final selected model. The traditional answer to this question is given by cross-validation. The cross-validation estimate of prediction error is nearly unbiased but can be highly variable. Here we discuss bootstrap estimates of prediction error, which can be thought of as smoothed versions of cross-validation. We show that a particular bootstrap method, the .632+ rule, substantially outperforms cross-validation in a catalog of 24 simulation experiments. Besides providing point estimates, we also consider estimating the variability of an error rate estimate. All of the results here are nonparametric and apply to any possible prediction rule; however, we study only classification problems with 0–1 loss in detail. Our simulations include “smooth” prediction rules like Fisher's linear discriminant fun...
1,602 citations
TL;DR: The generalized partially linear single-index model (GPLSIM) as discussed by the authors is a nonparametric generalized linear model for regression of a response Y on predictors (X, Z) with conditional mean function based on a linear combination of X, Z, where η 0(·) is an unknown function.
Abstract: The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α T 0X + β T 0Z by η0(α T 0X) + β T 0Z, where η0(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the “single-index” models, which have β0 = 0. Using local linear methods, we propose estimates of the unknown parameters (α0, β0) and the unknown function η0(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology.
794 citations
TL;DR: In this article, a Monte Carlo version of the EM algorithm was proposed and evaluated for a wide variety of problems where they were not previously, and the authors used the Newton-Raphson algorithm as a framework to compare maximum likelihood to the joint-maximization or penalized quasi-likelihood methods and explain why the latter can perform poorly.
Abstract: Maximum likelihood algorithms are described for generalized linear mixed models. I show how to construct a Monte Carlo version of the EM algorithm, propose a Monte Carlo Newton-Raphson algorithm, and evaluate and improve the use of importance sampling ideas. Calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously. I also use the Newton-Raphson algorithm as a framework to compare maximum likelihood to the “joint-maximization” or penalized quasi-likelihood methods and explain why the latter can perform poorly.
765 citations
TL;DR: In this paper, a Bayesian approach to shrinkage is proposed by placing priors on the wavelet coefficients, where the prior for each coefficient consists of a mixture of two normal distributions with different standard deviations.
Abstract: When fitting wavelet based models, shrinkage of the empirical wavelet coefficients is an effective tool for denoising the data. This article outlines a Bayesian approach to shrinkage, obtained by placing priors on the wavelet coefficients. The prior for each coefficient consists of a mixture of two normal distributions with different standard deviations. The simple and intuitive form of prior allows us to propose automatic choices of prior parameters. These parameters are chosen adaptively according to the resolution level of the coefficients, typically shrinking high resolution (frequency) coefficients more heavily. Assuming a good estimate of the background noise level, we obtain closed form expressions for the posterior means and variances of the unknown wavelet coefficients. The latter may be used to assess uncertainty in the reconstruction. Several examples are used to illustrate the method, and comparisons are made with other shrinkage methods.
577 citations
TL;DR: In this paper, the authors established nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect, and the bounds provided are the tightest possible, given the distribution of assignments, treatments, and responses.
Abstract: This article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect. The bounds provided are the tightest possible, given the distribution of assignments, treatments, and responses. The formulas show that even with high rates of noncompliance, experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population.
575 citations
TL;DR: In this paper, the posterior for the number of components in a mixture of normals is not well defined, and posterior simulation does not provide a direct estimate of the posterior of the components in the mixture.
Abstract: Mixtures of normals provide a flexible model for estimating densities in a Bayesian framework. There are some difficulties with this model, however. First, standard reference priors yield improper posteriors. Second, the posterior for the number of components in the mixture is not well defined (if the reference prior is used). Third, posterior simulation does not provide a direct estimate of the posterior for the number of components. We present some practical methods for coping with these problems. Finally, we give some results on the consistency of the method when the maximum number of components is allowed to grow with the sample size.
545 citations
TL;DR: This article extends existing hierarchical spatial models to account for temporal effects and spatio-temporal interactions andfits the resulting highly parameterized models using Markov chain Monte Carlo methods, as well as novel techniques for model evaluation and selection.
Abstract: Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with sociodemographic census information, they also permit assessment of environmental justice; that is, whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining geographic resolution. In this article we extend existing hierarchical spatial models to account for temporal effects and spatio-temporal interactions. Fitting the resulting highly parameterized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of county-specific lung cancer rates in the state of Ohio during the period 1968–1988.
TL;DR: In this paper, a data-determined method for testing structural models of the errors in vector autoregressions is discussed, which can easily be combined with prior economic knowledge and a subjective analysis of data characteristics to yield valuable information concerning model selection and specification.
Abstract: A data-determined method for testing structural models of the errors in vector autoregressions is discussed. The method can easily be combined with prior economic knowledge and a subjective analysis of data characteristics to yield valuable information concerning model selection and specification. In one dimension, it turns out that standard t statistics can be used to test the various overidentifying restrictions that are implied by a model. In another dimension, the method compares a priori knowledge of a structural model for the errors with the properties exhibited by the data. Thus this method may help to ensure that orderings of the errors for impulse response and forecast error variance decomposition analyses are sensible, given the data. Two economic examples are used to illustrate the method.
TL;DR: A class of performance indices based on posterior tail probabilities of relevant model parameters that indicate the degree of poor performance by a provider are proposed and applied to profile hospitals on the basis of 30-day mortality rates for a cohort of elderly heart attack patients.
Abstract: Recent public debate on costs and effectiveness of health care in the United States has generated a growing emphasis on “profiling” of medical care providers. The process of profiling involves comparing resource use and quality of care among medical providers to a community or a normative standard. This is valuable for targeting quality improvement strategies. For example, hospital profiles may be used to determine whether institutions deviate in important ways in the process of care they deliver. In this article we propose a class of performance indices to profile providers. These indices are based on posterior tail probabilities of relevant model parameters that indicate the degree of poor performance by a provider. We apply our performance indices to profile hospitals on the basis of 30-day mortality rates for a cohort of elderly heart attack patients. The analysis used data from 96 acute care hospitals located in one state and accounted for patient and hospital characteristics using a hierarc...
TL;DR: Markov processes for stochastic modeling, Markov Processes for Stochastic Modeling, اطلاعات رسانی کشاورزی, £1.5bn in order to model the response of the immune system to shocks in the presence of natural disasters.
Abstract: Markov processes for stochastic modeling , Markov processes for stochastic modeling , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
TL;DR: The concomitant latent class model for analyzing multivariate categorical outcome data is studied, and practical theory for reducing and identifying such models is developed.
Abstract: Quantifying human health and functioning poses significant challenges in many research areas. Commonly in the social and behavioral sciences and increasingly in epidemiologic research, multiple indicators are utilized as responses in lieu of an obvious single measure for an outcome of interest. In this article we study the concomitant latent class model for analyzing such multivariate categorical outcome data. We develop practical theory for reducing and identifying such models. We detail parameter and standard error fitting that parallels standard latent class methodology, thus supplementing the approach proposed by Dayton and Macready. We propose and study diagnostic strategies, exemplifying our methods using physical disability data from an ongoing gerontologic study. Throughout, the focus of our work is on applications for which a primary goal is to study the association between health or functioning and covariates.
TL;DR: The authors collected data on the one-year-ahead income expectations of members of American households in a survey of economic expectations (SEE), a module of a national continuous telephone survey conducted at the University of Wisconsin.
Abstract: We have collected data on the one-year-ahead income expectations of members of American households in our survey of economic expectations (SEE), a module of a national continuous telephone survey conducted at the University of Wisconsin. The income-expectations questions take this form: “What do you think is the percent chance (or what are the chances out of 100) that your total household income, before taxes, will be less than Y over the next 12 months?” We use the responses to a sequence of such questions posed for different income thresholds Y to estimate each respondent's subjective probability distribution for next year's household income. We use the estimates to study the cross-sectional variation in income expectations one year into the future. We find that the estimated subjective interquartile range (IQR) of future income tends to rise with the estimated subjective median, but more slowly than proportionately. There is substantial variation in the estimated subjective IQR among responden...
TL;DR: In this article, a binary procedure combined with the Schwarz information criterion (SIC) is used to search all of the possible variance changepoints existing in the sequence, and the results are applied to the weekly stock prices.
Abstract: This article explores testing and locating multiple variance changepoints in a sequence of independent Gaussian random variables (assuming known and common mean). This type of problem is very common in applied economics and finance. A binary procedure combined with the Schwarz information criterion (SIC) is used to search all of the possible variance changepoints existing in the sequence. The simulated power of the proposed procedure is compared to that of the CUSUM procedure used by Inclan and Tiao to cope with variance changepoints. The SIC and unbiased SIC for this problem are derived. To obtain the percentage points of the SIC criterion, the asymptotic null distribution of a function of the SIC is obtained, and then the approximate percentage points of the SIC are tabulated. Finally, the results are applied to the weekly stock prices. The unknown but common mean case is also outlined at the end.
TL;DR: The authors showed that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple-hypothesis testing situations, the Simes method indeed controls the probability of type I error.
Abstract: The Simes method for testing intersection of more than two hypotheses is known to control the probability of type I error only when the underlying test statistics are independent. Although this method is more powerful than the classical Bonferroni method, it is not known whether it is conservative when the test statistics are dependent. This article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple-hypothesis testing situations, the Simes method indeed controls the probability of type I error. This extends some results established very recently in the special case of two hypotheses.
TL;DR: In this article, a method for estimating the parameters and quantiles of the generalized Pareto distribution (GPD) has been proposed, and the estimators are well defined for all parameter values.
Abstract: The generalized Pareto distribution (GPD) was introduced by Pickands to model exceedances over a threshold. It has since been used by many authors to model data in several fields. The GPD has a scale parameter ([sgrave] > 0) and a shape parameter (−∞ 1, the maximum likelihood estimates do not exist, and when k is between 1/2 and 1, they may have problems. Furthermore, for k ≤ −1/2, second and higher moments do not exist, and hence both the method-of-moments (MOM) and the probability-weighted moments (PWM) estimates do not exist. Another and perhaps more serious problem with the MOM and PWM methods is that they can produce nonsensical estimates (i.e., estimates inconsistent with the observed data). In this article we propose a method for estimating the parameters and quantiles of the GPD. The estimators are well defined for all parameter values. They are also easy to compute. Some asymptotic results are provide...
TL;DR: This article constructs asymptotically valid prediction intervals and shows how to use the prediction intervals to choose the number of nodes in the network and applies the theory to an example for predicting the electrical load.
Abstract: The artificial neural network (ANN) is becoming a very popular model for engineering and scientific applications. Inspired by brain architecture, artificial neural networks represent a class of nonlinear models capable of learning from data. Neural networks have been applied in many areas, including pattern matching, classification, prediction, and process control. This article focuses on the construction of prediction intervals. Previous statistical theory for constructing confidence intervals for the parameters (or the weights in an ANN), is inappropriate, because the parameters are unidentifiable. We show in this article that the problem disappears in prediction. We then construct asymptotically valid prediction intervals and also show how to use the prediction intervals to choose the number of nodes in the network. We then apply the theory to an example for predicting the electrical load.
TL;DR: Part 1 Introduction: geographihcal epidemiology and ecological studies small-area studies - purpose and methods health and the environment - the significance of chemicals and radiation.
Abstract: Part 1 Introduction: geographihcal epidemiology and ecological studies small-area studies - purpose and methods health and the environment - the significance of chemicals and radiation. Part 2 Data, computational methods and mapping: mortality data cancer incidence data for adults cancer incidence data for children congenital anomalies specialized registers population counts in small areas use of routine data in studies of point sources of environmental pollution socio-economic confounding use of record linkage in small-area studies confidentiality practical approaches to disease mapping estimating environmental exposures mapping environmental exposure. Part 3 Statistical methods: statistical methods for geographical correlation studies Bayesian methods for mapping disease risk statistical methods for analyzing point-source exposures some comments on methods for investigating disease risk around a point source methods for the assessment of disease clusters. Part 4 Studies of health and the environment: environmental epidemiology - a historical perspective guidelines for the investigation of clusters of adverse health events studies of diseas clustering - problems of interpretation. Part 5 Case studies: childhood leukaemia around the Sellafield nuclear plant the epidemic of respiratory cancer associated with erionite fibres in the Cappadocian region of Turkey soya bean as a risk factor of epidemic asthma the Seveso accident cancer of the larynx and lung near incinerators of waste solvents and oils in Britain a study of geographical correlations in China.
TL;DR: In this paper, the authors considered fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregression conditional heteroScedastic (GARCH) and the fractional (ARMA) models.
Abstract: This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration,...
TL;DR: In this article, the authors consider the maximum likelihood estimation of the parameters in the proportional odds model with right-censored data and show that the estimator of the regression coefficient is asymptotically normal with efficient variance.
Abstract: We consider maximum likelihood estimation of the parameters in the proportional odds model with right-censored data. The estimator of the regression coefficient is shown to be asymptotically normal with efficient variance. The maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation. Estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent. A likelihood ratio test for the regression coefficient is also considered.
TL;DR: The empirical bias bandwidth selector (EBBS) as discussed by the authors minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term, where the bias term is estimated empirically, not from an asymptotic expression.
Abstract: A data-based local bandwidth selector is proposed for nonparametric regression by local fitting of polynomials. The estimator, called the empirical-bias bandwidth selector (EBBS), is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function. EBBS minimizes an estimate of mean squared error consisting of a squared bias term plus a variance term. The variance term used is exact, not asymptotic, though it involves the conditional variance of the response given the predictors that must be estimated. The bias term is estimated empirically, not from an asymptotic expression. Thus EBBS is similar to the “double smoothing” approach of Hardle, Hall, and Marron and a local bandwidth selector of Schucany, but is developed here for a far wider class of estimation problems than what those authors considered. EBBS is tested on simulated data, and its performance seems quite satisfactory. Local polynomial smoothing of a histogram is a high...
TL;DR: This paper used posterior simulation output to estimate integrated likelihoods for Bayesian hypothesis testing and model selection, and applied this estimator to data from the World Fertility Survey and showed it to give accurate results.
Abstract: The key quantity needed for Bayesian hypothesis testing and model selection is the integrated, or marginal, likelihood of a model. We describe a way to use posterior simulation output to estimate integrated likelihoods. We describe the basic Laplace—Metropolis estimator for models without random effects. For models with random effects, we introduce the compound Laplace-Metropolis estimator. We apply this estimator to data from the World Fertility Survey and show it to give accurate results. Batching of simulation output is used to assess the uncertainty involved in using the compound Laplace-Metropolis estimator. The method allows us to test for the effects of independent variables in a random-effects model and also to test for the presence of the random effects.
TL;DR: In this article, a time series of subtidal fluctuations at Crescent City, California, during 1980-1991 using the maximal overlap discrete wavelet transform (MODWT) was analyzed and it was shown that the variability in these fluctuations depends on the season for scales of 32 days and less.
Abstract: Subtidal coastal sea level fluctuations affect coastal ecosystems and the consequences of destructive events such as tsunamis. We analyze a time series of subtidal fluctuations at Crescent City, California, during 1980–1991 using the maximal overlap discrete wavelet transform (MODWT). Our analysis shows that the variability in these fluctuations depends on the season for scales of 32 days and less. We show how the MODWT characterizes nonstationary behavior succinctly and how this characterization can be used to improve forecasts of inundation during tsunamis and storm surges. We provide pseudocode and enough details so that data analysts in other disciplines can readily apply MODWT analysis to other nonstationary time series.
TL;DR: The proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded, such as when a patient dies or is discharged.
Abstract: In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, patients and data arrive sequentially, and new patient-specific parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for continuous updating of the evolving posterior distribution, but would need to be restarted from scratch at each expansion stage. Thus MCMC methods are often too slow for real-time inference in dynamic contexts. By combining MCMC with importance resampling, we show how real-time sequential updating of posterior distributions can be effected. The proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded, such as when a patient dies or is discharged. We apply the ...