scispace - formally typeset
Search or ask a question

Showing papers in "Journal of the American Statistical Association in 1989"



Journal ArticleDOI
TL;DR: In this article, the authors derived the asymptotic distribution of the maximum partial likelihood estimator β for the vector of regression coefficients β under a possibly misspecified Cox proportional hazards model.
Abstract: We derive the asymptotic distribution of the maximum partial likelihood estimator β for the vector of regression coefficients β under a possibly misspecified Cox proportional hazards model. As in the parametric setting, this estimator β converges to a well-defined constant vector β*. In addition, the random vector n 1/2(β – β*) is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated. The newly proposed robust covariance matrix estimator is similar to the so-called “sandwich” variance estimators that have been extensively studied for parametric cases. For many misspecified Cox models, the asymptotic limit β* or part of it can be interpreted meaningfully. In those circumstances, valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of β and the related results for the score statistics. Extensive studies demonstrate that the proposed robust tests and interval estimation procedures...

2,466 citations


Journal ArticleDOI
TL;DR: Alternatives to the usual maximum likelihood estimates for the covariance matrices are proposed, characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample-based estimate of future misclassification risk.
Abstract: Linear and quadratic discriminant analysis are considered in the small-sample, high-dimensional setting. Alternatives to the usual maximum likelihood (plug-in) estimates for the covariance matrices are proposed. These alternatives are characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample-based estimate of future misclassification risk. Computationally fast implementations are presented, and the efficacy of the approach is examined through simulation studies and application to data. These studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved.

2,440 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider the regression analysis of multivariate failure time observations and formulate each marginal distribution of the failure times by a Cox proportional hazards model, which is shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated.
Abstract: Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time observations. Each marginal distribution of the failure times is formulated by a Cox proportional hazards model. No specific structure of dependence among the distinct failure times on each subject is imposed. The regression parameters in the Cox models are estimated by maximizing the failure-specific partial likelihoods. The resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated. Simultaneous inferential procedures are then proposed. Extensive Monte Carlo studies indicate that the normal approximation is adequate for practical use. The new methods allow time-dependent covariates, missing observations, and arbitrary patterns of censorship. They are illustrat...

1,861 citations


Journal ArticleDOI
TL;DR: The theoretical and practical issues encountered in conducting the matching operation and the results of that operation are discussed.
Abstract: A test census of Tampa, Florida and an independent postenumeration survey (PES) were conducted by the U.S. Census Bureau in 1985. The PES was a stratified block sample with heavy emphasis placed on hard-to-count population groups. Matching the individuals in the census to the individuals in the PES is an important aspect of census coverage evaluation and consequently a very important process for any census adjustment operations that might be planned. For such an adjustment to be feasible, record-linkage software had to be developed that could perform matches with a high degree of accuracy and that was based on an underlying mathematical theory. A principal purpose of the PES was to provide an opportunity to evaluate the newly implemented record-linkage system and associated methodology. This article discusses the theoretical and practical issues encountered in conducting the matching operation and presents the results of that operation. A review of the theoretical background of the record-linkage...

1,347 citations


Journal ArticleDOI
TL;DR: In this paper, an analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate non-linear regression.
Abstract: The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate nonlinear regression. The degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference, with moderate increases in computational complexity for many models. Estimation of precision from asymptotic theory and the bootstrap is discussed, and graphical methods for checking the appropriateness of the t distribution are presented.

1,336 citations


Journal ArticleDOI
TL;DR: In this paper, a simple yet widely applicable model-building procedure for threshold autoregressive models is proposed based on some predictive residuals, and a simple statistic is proposed to test for threshold nonlinearity and specify the threshold variable.
Abstract: The threshold autoregressive model is one of the nonlinear time series models available in the literature. It was first proposed by Tong (1978) and discussed in detail by Tong and Lim (1980) and Tong (1983). The major features of this class of models are limit cycles, amplitude dependent frequencies, and jump phenomena. Much of the original motivation of the model is concerned with limit cycles of a cyclical time series, and indeed the model is capable of producing asymmetric limit cycles. The threshold autoregressive model, however, has not received much attention in application. This is due to (a) the lack of a suitable modeling procedure and (b) the inability to identify the threshold variable and estimate the threshold values. The primary goal of this article, therefore, is to suggest a simple yet widely applicable model-building procedure for threshold autoregressive models. Based on some predictive residuals, a simple statistic is proposed to test for threshold nonlinearity and specify the ...

977 citations


ReportDOI
TL;DR: In this article, the authors explore the value of simple specification tests in selecting an appropriate nonex-experiment estimator for a manpower training program and find that a simple testing procedure eliminates the range of nonexperimental estimators at variance with the experimental estimates of program impact.
Abstract: The recent literature on evaluating manpower training programs demonstrates that alternative nonexperimental estimators of the same program produce an array of estimates of program impact. These findings have led to the call for experiments to be used to perform credible program evaluations. Missing in all of the recent pessimistic analyses of nonexperimental methods is any systematic discussion of how to choose among competing estimators. This article explores the value of simple specification tests in selecting an appropriate nonexperimental estimator. A reanalysis of the National Supported Work Demonstration data previously analyzed by proponents of social experiments reveals that a simple testing procedure eliminates the range of nonexperimental estimators at variance with the experimental estimates of program impact.

876 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed a set of tests for detecting possible changes in parameters when the observations are obtained sequentially in time, where the alternative one has in mind specifies the parameter process as a martingale.
Abstract: Tests are proposed for detecting possible changes in parameters when the observations are obtained sequentially in time. While deriving the tests the alternative one has in mind specifies the parameter process as a martingale. The distribution theory of these tests relies on the large-sample results; that is, only the limiting null distributions are known (except in very special cases). The main tool in establishing these limiting distributions is weak convergence of stochastic processes. Suppose that we have vector-valued observations x 1, …, x n obtained sequentially in time (or ordered in some other linear fashion). Their joint distribution is described by determining the initial distribution for x 1 and the conditional distribution for each x k given the past up to x k–1. Suppose further that these distributions depend on a p-dimensional parameter vector θ. At least locally (i.e., in a short time period) this may be more or less legitimate. In the long run, however, the possibility of some ch...

848 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider the class of bivariate survival distributions that can arise in this way, and show that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter.
Abstract: When two observed survival times depend via a proportional-hazards model on the same unobserved variable, called a frailty, this common dependence induces an association between the observed times. This article considers the class of bivariate survival distributions that can arise in this way, extends it to allow negative association, and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter. A cross-ratio function, easily estimated even from censored data, is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples. The models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data. The main distinguishing feature of survival data is the possibility of censoring, which makes the standard methods difficu...

832 citations




Journal ArticleDOI
TL;DR: In this paper, optimal matched samples are obtained using network flow theory, which yields optimal constructions for several statistical matching problems that have not been studied previously, including the construction of matched samples with multiple controls, with a variable number of controls, and the balanced matched samples that combine features of pair matching and frequency matching.
Abstract: Matching is a common method of adjustment in observational studies. Currently, matched samples are constructed using greedy heuristics (or “stepwise” procedures) that produce, in general, suboptimal matchings. With respect to a particular criterion, a matched sample is suboptimal if it could be improved by changing the controls assigned to specific treated units, that is, if it could be improved with the data at hand. Here, optimal matched samples are obtained using network flow theory. In addition to providing optimal matched-pair samples, this approach yields optimal constructions for several statistical matching problems that have not been studied previously, including the construction of matched samples with multiple controls, with a variable number of controls, and the construction of balanced matched samples that combine features of pair matching and frequency matching. Computational efficiency is discussed. Extensive use is made of ideas from two essentially disjoint literatures, namely st...

Journal ArticleDOI
TL;DR: Inverse Gaussian distributions have been used for life testing and reliability as mentioned in this paper, and they have been applied in a variety of applications, such as life testing, reliability, and life assurance.
Abstract: 1. Introduction 2. Properties of the Inverse Gaussian Distribution 3. Genesis 4. Certain Useful Transformations and Characterizations 5. Sampling and Estimation of Parameters 6. Significance Tests 7. Bayesian Inference 8. Regression Analysis 9. Life Testing and Reliability 10. Applications 11. Additional Topics

Journal ArticleDOI
TL;DR: Unimodality of Discrete Distributions as mentioned in this paper is a generalization of the notion of infinite-divergences in the context of univariate unimodal distributions.
Abstract: Properties of Univariate Unimodal Distributions. Concepts of Multivariate Unimodality. Some More Notions of Unimodality. Unimodality for Discrete Distributions. Unimodality of Infinitely Divisible Distributions. Unimodality and Notions of Dependence. Ordering of Distributions by Peakedness. Applications of Unimodality in Statistical Inference. Convexity in Reliability Theory. Appendix.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the properties of a recursive estimation procedure (the method of "back-propagation") for a class of nonlinear regression models (single hidden-layer feedforward network models) recently developed by cognitive scientists.
Abstract: We investigate the properties of a recursive estimation procedure (the method of “back-propagation”) for a class of nonlinear regression models (single hidden-layer feedforward network models) recently developed by cognitive scientists. The results follow from more general results for a class of recursive m estimators, obtained using theorems of Ljung (1977) and Walk (1977) for the method of stochastic approximation. Conditions are given ensuring that the back-propagation estimator converges almost surely to a parameter value that locally minimizes expected squared error loss (provided the estimator does not diverge) and that the back-propagation estimator is asymptotically normal when centered at this minimizer. This estimator is shown to be statistically inefficient, and a two-step procedure that has efficiency equivalent to that of nonlinear least squares is proposed. Practical issues are illustrated by a numerical example involving approximation of the Henon map.

Journal ArticleDOI
TL;DR: In this paper, conditionally independent hierarchical models of the kind used in parametric empirical Bayes (PEB) methodology are considered, where the observation vectors Yi for units i = 1, …, k are independently distributed with densities p(yi | θi, λ).
Abstract: We consider two-stage models of the kind used in parametric empirical Bayes (PEB) methodology, calling them conditionally independent hierarchical models. We suppose that there are k “units,” which may be experimental subjects, cities, study centers, etcetera. At the first stage, the observation vectors Yi for units i = 1, …, k are independently distributed with densities p(yi | θi ), or more generally, p(yi | θi, λ). At the second stage, the unit-specific parameter vectors θi are iid with densities p(θi | λ). The PEB approach proceeds by regarding the second-stage distribution as a prior and noting that, if λ were known, inference about θ could be based on its posterior. Since λ is not known, the simplest PEB methods estimate the parameter λ by maximum likelihood or some variant, and then treat λ as if it were known to be equal to this estimate. Although this procedure is sometimes satisfactory, a well-known defect is that it neglects the uncertainty due to the estimation of λ. In this article w...

Journal ArticleDOI
TL;DR: In this article, the authors examined some problems of significance testing for one-sided hypotheses of the form H 0 : θ ≤ θ 0 versus H 1: θ > θ 1, where θ is the parameter of interest, and provided a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions.
Abstract: This article examines some problems of significance testing for one-sided hypotheses of the form H 0 : θ ≤ θ 0 versus H 1 : θ > θ 0, where θ is the parameter of interest. In the usual setting, let x be the observed data and let T(X) be a test statistic such that the family of distributions of T(X) is stochastically increasing in θ. Define Cx as {X : T(X) — T(x) ≥ 0}. The p value is p(x) = sup θ≤θ0 Pr(X ∈ Cx | θ). In the presence of a nuisance parameter η, there may not exist a nontrivial Cx with a p value independent of η. We consider tests based on generalized extreme regions of the form Cx (θ, η) = {X : T(X; x, θ, η) ≥ T(x; x, θ, η)}, and conditions on T(X; x, θ, η) are given such that the p value p(x) = sup θ≤θ0 Pr(X ∈ Cx (θ, η)) is free of the nuisance parameter η, where T is stochastically increasing in θ. We provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions, a problem for which the fixed-level testing approach...

Journal ArticleDOI
TL;DR: In this paper, the authors extend the fully exponential method to apply to expectations and variances of nonpositive functions, and obtain a second-order approximation to an expectation E(g(θ).
Abstract: Tierney and Kadane (1986) presented a simple second-order approximation for posterior expectations of positive functions They used Laplace's method for asymptotic evaluation of integrals, in which the integrand is written as f(θ)exp(-nh(θ)) and the function h is approximated by a quadratic The form in which they applied Laplace's method, however, was fully exponential: The integrand was written instead as exp[− nh(θ) + log f(θ)]; this allowed first-order approximations to be used in the numerator and denominator of a ratio of integrals to produce a second-order expansion for the ratio Other second-order expansions (Hartigan 1965; Johnson 1970; Lindley 1961, 1980; Mosteller and Wallace 1964) require computation of more derivatives of the log-likelihood function In this article we extend the fully exponential method to apply to expectations and variances of nonpositive functions To obtain a second-order approximation to an expectation E(g(θ)), we use the fully exponential method to approximate

Journal ArticleDOI
TL;DR: In this article, a reference prior for the problem of estimating the hatching rate of larvae per unit area is proposed, which is based on the product of the mean of the number of larvae hatching per mass and the mean number of masses being hatched per mass.
Abstract: Suppose that we observe X ∼ N(α, 1) and, independently, Y ∼ N(β, 1), and are concerned with inference (mainly estimation and confidence statements) about the product of means θ = αβ. This problem arises, most obviously, in situations of determining area based on measurements of length and width. It also arises in other practical contexts, however. For instance, in gypsy moth studies, the hatching rate of larvae per unit area can be estimated as the product of the mean of egg masses per unit area times the mean number of larvae hatching per egg mass. Approximately independent samples can be obtained for each mean (see Southwood 1978). Noninformative prior Bayesian approaches to the problem are considered, in particular the reference prior approach of Bernardo (1979). An appropriate reference prior for the problem is developed, and relatively easily implementable formulas for posterior moments (e.g., the posterior mean and variance) and credible sets are derived. Comparisons with alternative noninf...

Journal ArticleDOI
TL;DR: In this article, the authors developed tests for detecting extra-Poisson variation in counting data, which can be obtained as score tests against arbitrary mixed Poisson alternatives and are generalizations of tests of Fisher (1950) and Collings and Margolin (1985).
Abstract: Poisson regression models are widely used in analyzing count data. This article develops tests for detecting extra-Poisson variation in such situations. The tests can be obtained as score tests against arbitrary mixed Poisson alternatives and are generalizations of tests of Fisher (1950) and Collings and Margolin (1985). Accurate approximations for computing significance levels are given, and the power of the tests against negative binomial alternatives is compared with those of the Pearson and deviance statistics. One way to test for extra-Poisson variation is to fit models that parametrically incorporate and then test for the absence of such variation within the models; for example, negative binomial models can be used in this way (Cameron and Trivedi 1986; Lawless 1987a). The tests in this article require only the Poisson model to be fitted. Two test statistics are developed that are motivated partly by a desire to have good distributional approximations for computing significance levels. Simu...


Journal ArticleDOI
TL;DR: In this paper, the authors discuss measures of multivariate dependence and measures of conditional dependence based on relative entropies, which are conceptually very general, as they can be used for a set of variables that can be a mixture of continuous, ordinal-categorical, and nominal-Categorical variables.
Abstract: There has been a lot of work on measures of dependence or association for bivariate probability distributions or bivariate data. These measures usually assume that the variables are both continuous or both categorical. In comparison, there is very little work on multivariate or conditional measures of dependence. The purpose of this article is to discuss measures of multivariate dependence and measures of conditional dependence based on relative entropies. These measures are conceptually very general, as they can be used for a set of variables that can be a mixture of continuous, ordinal-categorical, and nominal-categorical variables. For continuous or ordinal-categorical variables, a certain transformation of relative entropy to the interval [0, 1] leads to generalizations of the correlation, multiple-correlation, and partial-correlation coefficients. If all variables are nominal categorical, the relative entropies are standardized to take a maximum of 1 and then transformed so that in the bivar...

Journal ArticleDOI
TL;DR: Problems of estimation when initiating events occur as a nonhomogeneous Poisson process are considered, and the time from the initiating event to the final event has pdf f(s) independent of the time of the initiatingevent.
Abstract: In some epidemiologic studies, identification of individuals for study is dependent on the occurrence of some event. Once an individual is identified, the time of a previous event, termed an initiating event, is determined retrospectively. This article considers problems of estimation when initiating events occur as a nonhomogeneous Poisson process, and the time s from the initiating event to the final event has pdf f(s) independent of the time of the initiating event. A simple form for the likelihood function is obtained and methods of parametric and nonparametric estimation are developed and considered. In particular, the model is related to a Poisson process in the plane, and for the parametric case simple algorithms are developed for parameter estimation. Regression models are also considered as well as various generalizations of the basic problem. Parallel to the theoretical development, data on patients diagnosed with acquired immune deficiency syndrome (AIDS) are considered and a detailed ...



Journal ArticleDOI
TL;DR: The result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages.
Abstract: A new result dealing with smoothing and interpolation in the state-space model is developed and explored. The result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages. The connection to signal extraction and interpolation is explored, and diffuse specifications are considered.

Journal ArticleDOI
TL;DR: In this paper, a score test for autocorrelation in the within-individual errors for the conditional independence random effects model was developed and an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and AR(1) errors was derived.
Abstract: For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the “conditional independence” random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregressive) AR(1) errors is then derived. Empirical Bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with AR(1) errors model are also considered. A numerical example is presented to illustrate these methods.

Journal ArticleDOI
TL;DR: In this article, accumulated sudden infant death syndrome (SIDS) data, from 1974-1978 and 1979-1984 for the counties of North Carolina, are analyzed, and Markov random-field models are fit to the data.
Abstract: In this article, accumulated sudden infant death syndrome (SIDS) data, from 1974–1978 and 1979–1984 for the counties of North Carolina, are analyzed. After a spatial exploratory data analysis, Markov random-field models are fit to the data. The (spatial) trend is meant to capture the large-scale variation in the data, and the variance and spatial dependence are meant to capture the small-scale variation. The trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location. Both models are fit and compared. The results give an excellent illustration of a phenomenon already well-known in time series, that autocorrelation in data can be due to an undiscovered explanatory variable. Indeed, for 1974–1978 we confirm a dependence of SIDS rate on proportion of nonwhite babies born, along with insignificant spatial correlation. Without this regressor variable, however, the spatial correlation is significant. In 1979–1984, perhaps due to reporting bias o...

BookDOI
TL;DR: In this article, the authors focus on limiting the distribution of variance of Kernel-Type Density Estimators in the norm of the space C and L 2 of a regression curve.
Abstract: 1. Asymptotic Properties of Certain Measures of Deviation for Kernel-Type Non Parametric Estimators of Probability Densities.- 1. Integrated Mean Square Error of Nonparametric Kernel-Type Probability Density Estimators.- 2. The Mean Square Error of Nonparametric Kernel-Type Density Estimators.- 2. Strongly Consistent in Functional Metrics Estimators of Probability Density.- 1. Strong Consistency of Kernel-Type Density Estimators in the Norm of the Space C.- 2. Convergence in the L2 Norm of Kernel-Type Density Estimators.- 3. Convergence in Variation of Kernel-Type Density Estimators and its Application to a Nonparametric Estimator of Bayesian Risk in a Classification Problem.- 3. Limiting Distributions of Deviations of Kernel-Type Density Estimators.- 1. Limiting Distribution of Maximal Deviation of Kernel-Type Estimators.- 2. Limiting Distribution of Quadratic Deviation of Two Nonparametric Kernel-Type Density Estimators.- 3. The Asymptotic Power of the Un1n2-Test in the Case of' singular' Close Alternatives.- 4. Testing for Symmetry of a Distribution.- 5. Independence of Tests Based on Kernel-Type Density Estimators.- 4. Nonparametric Estimation of the Regression Curve and Components of a Convolution.- 1. Some Asymptotic Properties of Nonparametric Estimators of Regression Curves.- 2. Strong Consistency of Regression Curve Estimators in the Norm of the Space C(a, b).- 3. Limiting Distribution of the Maximal Deviation of Estimators of Regression Curves.- 4. Limiting Distribution of Quadratic Deviation of Estimators of Regression Curves.- 5. Nonparametric Estimators of Components of a Convolution (S.N. Bernstein's Problem).- 5. Projection Type Nonparametric Estimation of Probability Density.- 1. Consistency of Projection-Type Probability Density Estimator in the Norms of Spaces C and L2.- 2. Limiting Distribution of the Squared Norm of a Projection-Type Density Estimator.- Addendum Limiting Distribution of Quadratic Deviation for a Wide Class of Probability Density Estimators.- 1. Limiting Distribution of Un.- 2. Kernel Density Estimators / Rosenblatt-Parzen Estimators.- 3. Projection Estimators of Probability Density / Chentsov Estimators.- 4. Histogram.- 5. Deviation of Kernel Estimators in the Sence of the Hellinger Distance.- References.- Author Index.