Empirical Bayes regression analysis with many regressors but fewer observations |
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Authors: | Muni S Srivastava Tatsuya Kubokawa |
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Institution: | 1. Department of Statistics, University of Toronto, 100 St. George Street, Toronto, Ont., Canada M5S 3G3;2. Faculty of Economics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan |
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Abstract: | In this paper, we consider the prediction problem in multiple linear regression model in which the number of predictor variables, p, is extremely large compared to the number of available observations, n . The least-squares predictor based on a generalized inverse is not efficient. We propose six empirical Bayes estimators of the regression parameters. Three of them are shown to have uniformly lower prediction error than the least-squares predictors when the vector of regressor variables are assumed to be random with mean vector zero and the covariance matrix (1/n)XtX where Xt=(x1,…,xn) is the p×n matrix of observations on the regressor vector centered from their sample means. For other estimators, we use simulation to show its superiority over the least-squares predictor. |
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Keywords: | primary 62C12 62J07 secondary 62F10 62C20 |
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