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Minimax Multivariate Empirical Bayes Estimators under Multicollinearity
Srivastava, M. S.
98302
Kubokawa, Tatsuya
98303
330
Ernpirical Bayes estimator
ridge regression estimator
multicollinearity
multivariate linear regression model
multivariate normal distribution
application/pdf
In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions,that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases.
Journal of Multivariate Analysis, 2004. 掲載予定.
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technical report
日本経済国際共同センター
2002-12
Discussion paper series. CIRJE-F
2002-CF-187
AA11450569
eng
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2002/2002cf187ab.html
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