PREDICTION IN MULTIVARIATE MIXED LINEAR MODELS

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概要

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• In the multivariate mixed linear model or multivariate components of variance model with equal replications, this paper addresses the problem of predicting the sum of the regression mean and the random effects. When the feasible best linear unbiased predictors or empirical Bayes predictors are used, this prediction problem reduces to the estimation of the ratio of two covariance matrices. We propose scale equivariant shrinkage estimators for the ratio of the two covariance matrices. Their dominance properties over the usual estimators including the unbiased one are established, and further domination results are shown by using information of order restriction between the two covariance matrices. It is also demonstrated that the empirical Bayes predictors that employ these improved estimators of the ratio of the two covariance matrices have uniformly smaller risks than the crude Efron-Morris type estimator in the context of estimation of a mean matrix in a fixed effects linear regression model where the components are unknown parameters.

• 一般社団法人日本統計学会の論文

著者

• Srivastava Muni

  Department of Statistics, University of Toronto

• Srivastava Muni

  Department Of Statistics University Of Toronto

• KUBOKAWA Tatsuya

  Faculty of Economics, University of Tokyo

• Kubokawa Tatsuya

  Faculty Of Economics University Of Tokyo

関連論文

• Variable Selection in Multivariate Linear Regression Models with Fewer Observations than the Dimension
• CLASSIFICATION WITH A PREASSIGNED ERROR RATE WHEN TWO COVARIANCE MATRICES ARE EQUAL (Statistical Region Estimation and Its Application)
• PROFILE ANALYSIS FOR A GROWTH CURVE MODEL
• AN EMPIRICAL BAYES INFORMATION CRITERION FOR SELECTING VARIABLES IN LINEAR MIXED MODELS
• AKAIKE INFORMATION CRITERION FOR SELECTING COMPONENTS OF THE MEAN VECTOR IN HIGH DIMENSIONAL DATA WITH FEWER OBSERVATIONS
• COMPARISON OF DISCRIMINATION METHODS FOR HIGH DIMENSIONAL DATA
• PREDICTION IN MULTIVARIATE MIXED LINEAR MODELS
• ESTIMATION OF BOUNDED LOCATION AND SCALE PARAMETERS
• MINIMAXITY IN ESTIMATION OF RESTRICTED PARAMETERS
• ESTIMATION OF VARIANCE AND COVARIANCE COMPONENTS IN ELLIPTICALLY CONTOURED DISTRIBUTIONS
• CHARACTERIZATION OF PRIORS IN THE STEIN PROBLEM
• INTEGRAL INEQUALITY FOR MINIMAXITY IN THE STEIN PROBLEM
• SOME TESTS CONCERNING THE COVARIANCE MATRIX IN HIGH DIMENSIONAL DATA
• Estimation of EPMC for High-dimensional Data(Session 3b)
• PROFILE ANALYSIS WITH RANDOM-EFFECTS COVARIANCE STRUCTURE

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