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On marginal quasi-likelihood inference in generalized linear mixed models

JOURNAL OF MULTIVARIATE ANALYSIS 2001年第1期76卷 1-34页

作者： Sutradhar, BC Rao, RP Mem Univ Newfoundland Dept Math & Stat St Johns NF A1C 5S7 Canada Sri Sathya Sai Inst Higher Learning Anantapur Andhra Pradesh India

In view of the cumbersome and often intractable numerical integrations required For a Full likelihood analysis, several suggestions have been made recently fur approximate inference in generalized linear mixed models (GLMMs). Tao closely related approximate methods ale the penalized quasi-likelihood (PQL) method and the marginal quasi-likelihood (MQL) method. The PQL approach generally produces biased estimates Tol the regression effects and the variance component of the random effects. Recently, some corrections have been proposed to remove these biases. Rut the corrections appear. to he satisfactory only when the variance component of the random effects is small. The MQL approach has also been used fur inference in the GLMMs. This approach requires the computations of the joint moments of the clustered observations, up to order Four. But the derivation of these moments are not easy. Consequently, different "working" formulas have been used, especially For the mean and covariance matrix of the observations, which may not lead to desirable estimates. In this: paper. we use a small variance component (of the random effects) approach and develop the MQL estimating equations for the parameters based on the joint moments of order up to four. Thc proposed approach thus avoids the use of the so-called "working" covariance and higher order moment matrices, leading to better estimates for the regression and the overdispersion parameters, in the sense of efficiently in particular. (C) 2001 Academic Press AMS 1991 subject classifications: Primary 62A10;Secondary 62F11 ,62F12.

关键词： regression parameters variance component of the random effects quasi-likelihood estimation consistency improved efficiency

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Empirical likelihood for linear regression models under imputation for missing responses

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2001年第4期29卷 597-608页

作者： Wang, QH Rao, JNK Chinese Acad Sci Acad Math & Syst Sci Beijing 100080 Peoples R China

The authors study the empirical likelihood method for linear regression models. They show that when missing responses are imputed using least squares predictors, the empirical log-likelihood ratio is asymptotically a weighted sum of chi-square variables with unknown weights. They obtain an adjusted empirical log-likelihood ratio which is asymptotically standard chi-square and hence can be used to construct confidence regions. They also obtain a bootstrap empirical log-likelihood ratio and use its distribution to approximate that of the empirical log-likelihood ratio. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths of confidence intervals, and perform better than a normal approximation based method.

关键词： confidence intervals empirical likelihood linear regression imputation missing response regression parameters

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Semiparametric Bayesian inference for regression models

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 1999年第4期27卷 719-734页

作者： Seifu, Y Severini, TA Tanner, MA Univ New Brunswick Dept Math & Stat Fredericton NB E3B 5A3 Canada

This paper presents a method for Bayesian inference for the regression parameters in a linear model with independent and identically distributed errors that does not require the specification of a parametric family of densities for the error distribution. This method first selects a nonparametric kernel density estimate of the error distribution which is unimodal and based on the least-squares residuals. Once the error distribution is selected, the. Metropolis algorithm is used to obtain the marginal posterior distribution of the regression parameters. The methodology is illustrated with data sets, and its performance relative to standard Bayesian techniques is evaluated using simulation results.

关键词： Bayesian inference kernel density estimate Metropolis algorithm nonparametric regression parameters

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Comment analyser les donnees chronologiques pour plan partitionne en sciences sociales

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Bulletin de Méthodologie Sociologique 1999年第1期61卷 53-69页

作者： Clavet, Michel Petry, François Brien, Jean-Sébastien Département de science politique DKN 2460 Université Laval United Kingdom Département de science politique Université Laval United Kingdom Bureau de la statistique du Québec Canada

How to Analyze Time-Series Cross-Section Data in the Social Sciences. In this paper we present, step by step, a SAS statistical program for the analysis of Time-Series Cross-Section (TSCS) data which gives robust and unbiased regression estimates. Several statistical packages (SHAZAM. SAS. SPSS) offer procedures for the analysis of TSCS data based entirely, or in part, on a particular application of the Generalized Least Squares (GLS) method developed by Parks and Kmenta. In a series of recent articles. Beck and Katz have shown that the GLS estimation method often underestimates substantially the standard error of regression parameters in TSCS models. They suggest a new method for generating adequate correction of the error process in TSCS models. This method consists of using Ordinary Least Squares (OLS) parameter estimates first. and then replacing OLS standards errors (which are biased) with unbiased Panel-Corrected Standard Errors (PCSEs) obtained after correcting both temporal autocorrelation and spatial correlation structures. The paper provides a SAS application of the method suggested by Beck and Katz. The SAS program can be downloaded through our web site. © 1999, Sage Publications. All rights reserved.

关键词： Panel-Corrected Standard Errors regression parameters Standard Errors Time-Series Cross-Section (TSCS) Data Analysis

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Simultaneous equivariant estimation of the parameters of linear models

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STATISTICAL PAPERS 1998年第2期39卷 125-134页

作者： Bai, SK Durairajan, TM Loyola Coll Dept Stat Madras 600034 Tamil Nadu India

Consider a family of distributions which is invariant under a group of transformations. In this paper, we define an optimality criterion with respect to an arbitrary convex loss function and we prove a characterization theorem for an equivariant estimator to be optimal. Then we consider a linear model Y = X beta + epsilon, in which epsilon has a multivariate distribution with mean vector zero and has a density belonging to a scale family with scale parameter sigma. Also we assume that the underlying Family of distributions is invariant with respect to a certain group of transformations. First, we find the class of all equivariant estimators of regression parameters and the powers of sigma. By using the characterization theorem we discuss the simultaneous equivariant estimation of the parameters of the linear model.

关键词： convex loss function equivariant estimators characterization linear model regression parameters

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Asymptotical analysis of semiparametric models in survival analysis and accelerated life testing

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STATISTICS 1997年第3期29卷 261-283页

作者： Bagdonavicius, V Nikulin, M UNIV BORDEAUX 2 UFRMI 2SF-33076 BORDEAUXFRANCE

Classes of semiparametric models, generalizing the proportional and additive hazards, proportional odds and other models are considered. Asymptotical properties of estimators of regression parameters and baseline surv... 详细信息

关键词： semiparametric models survival analysis accelerated life testing regression parameters baseline function Cox model

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Analysing exponential family based messy data

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Communications in Statistics - Theory and Methods 1995年第10期24.0卷 2683-2699页

作者： Sutradhar, Brajendra C. Das, Kalyan Department of Mathematics and Statistics Memorial University of Newfoundland St. John's NF A1C 5S7 Canada Department of Statistics University of Calcutta Calcutta India

Recently exponential family based random effects models have received considerable attention. These models usually arise from an unobservable random process added to the independent exponential family models. An unobservable correlated process, however, would cause correlations among the exponential family based data. This paper, first, develops an asymptotically optimal test for testing the appropriateness of a fixed effects model for the exponential family based independent data versus a random effects model for the exponential family based independent or correlated data. The paper, then, provides a general framework on regression analysis for the exponential family based data generated under the random effects models. © 1995, Taylor & Francis Group, LLC. All rights reserved.

关键词： consistent estimates exponential family based correlated data latent correlated noise process messy parameter regression parameters score test

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TIME INTEGRATED LEAST-SQUARES ESTIMATORS OF regression parameters OF INDEPENDENT STOCHASTIC-PROCESSES

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 1990年第1期35卷 141-148页

作者： WU, TJ WASAN, MT QUEENS UNIV DEPT MATH & STATKINGSTON K7L 3N6ONTARIOCANADA

Industrial processes may be continuously monitored by instruments under control of microprocessors. Thus the data are usually obtained in the form of sets of (continuous) curves over certain time intervals. This paper presents a method of estimating regression parameters in terms of the sample paths from independent stochastic processes. Time integrated least squares estimators of the parameters are obtained which are unbiased, translation invariant, consistent and asymptotically jointly normal. Since technically it is difficult to compute these estimators, using analog-to-digital conversion of continuous processes which are time sampled at regular intervals, optimal approximations of the estimators are considered which are very easily computable and their asymptotic properties are appended.

关键词： time integrated process regression parameters sample paths of stochastic processes

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Sequential Shrinkage Estimation of Linear regression parameters

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Sequential Analysis 1987年第2期6卷 93-117页

作者： Nickerson, David M. Department of Statistics University of Florida Department of Statistics University of Georgia Athens Georgia 30602 Gainesville Florida 32611 Georgia

The paper considers estimation of p(>3) linear regression parameters (including the mean) under sequential sampling in a Gauss-Markoff setup. A class of James-Stein estimators that dominates the least squares estimator is developed, and an asymptotic risk expansion is given for both the least squares and James-Stein estimators. © 1987, Taylor & Francis Group, LLC. All rights reserved.

关键词： asymptotic risk expansion estimatoris Gauss-Markoff setup James -Stein least squares regression parameters sequential estimation submaritingales

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Sequential shrinkage estimation in the general linear. model

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Sequential Analysis 1988年第2期7卷 149-163页

作者： Sriram, T.N. Bose, Arup Department of statistics Purdue University West Lafayette IN 47907-2005 United States

The paper considers the estimation of the slope parameter βЄRK for k > 3, in a general linear model. A class of James-Stein estimators is proposed and is compared with the least squares estimator under an appropri... 详细信息

The paper considers the estimation of the slope parameter βЄR^K for k > 3, in a general linear model. A class of James-Stein estimators is proposed and is compared with the least squares estimator under an appropriate stopping rule. It is shown that the sequential James-Stein estimator dominates the sequential least, squares estimator. Furthermore, under mild regularity conditions, a second order asymptotic risk expansion for the sequential James-Stein estimator is obtained. Copyright © 1988, Taylor & Francis Group, LLC. All rights reserved.

关键词： expansion James-Stein estimators regression parameters reverse submartingales risk

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