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Estimating Risk and the Mean Squared Error Matrix in Stein Estimation

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  • Kubokawa, T.
  • Srivastava, M. S.

Abstract

It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative values with positive probability. In this paper, improved truncated estimators of the risk, risk difference, and MSE matrix are proposed and shown to be better than the UMVU estimators in terms of mean squared error.

Suggested Citation

  • Kubokawa, T. & Srivastava, M. S., 2002. "Estimating Risk and the Mean Squared Error Matrix in Stein Estimation," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 39-64, July.
    • Handle: RePEc:eee:jmvana:v:82:y:2002:i:1:p:39-64
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    References listed on IDEAS

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    1. Carter, R.A.L. & Srivastava, M.S. & Srivastava, V.K. & Ullah, A., 1990. "Unbiased Estimation of the MSE Matrix of Stein-Rule Estimators, Confidence Ellipsoids, and Hypothesis Testing," Econometric Theory, Cambridge University Press, vol. 6(1), pages 63-74, March.
    2. Konno, Yoshihiko, 1991. "On estimation of a matrix of normal means with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 44-55, January.
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    4. Kleffe, J. & Rao, J. N. K., 1992. "Estimation of mean square error of empirical best linear unbiased predictors under a random error variance linear model," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 1-15, October.
    5. Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
    6. Leo Breiman & Jerome H. Friedman, 1997. "Predicting Multivariate Responses in Multiple Linear Regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 3-54.
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