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On shrinkage estimators in matrix variate elliptical models

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  • M. Arashi
  • B. Kibria

  • A. Tajadod

Abstract

This paper derives the risk functions of a class of shrinkage estimators for the mean parameter matrix of a matrix variate elliptically contoured distribution. It is showed that the positive rule shrinkage estimator outperformed the shrinkage and unrestricted (maximum likelihood) estimators. To illustrate the findings of the paper, the relative risk functions for different degrees of freedoms are given for a multivariate t distribution. Shrinkage estimators for the matrix variate regression model under matrix normal, matrix t or Pearson VII error distributions would be special cases of this paper. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • M. Arashi & B. Kibria & A. Tajadod, 2015. "On shrinkage estimators in matrix variate elliptical models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 29-44, January.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:1:p:29-44
    DOI: 10.1007/s00184-014-0488-6
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    References listed on IDEAS

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    1. A. Saleh & Jan Picek & Jan Kalina, 2012. "R-estimation of the parameters of a multiple regression model with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 311-328, April.
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    3. Ohtani, Kazuhiro, 1993. "A Comparison of the Stein-Rule and Positive-Part Stein-Rule Estimators in a Misspecified Linear Regression Model," Econometric Theory, Cambridge University Press, vol. 9(4), pages 668-679, August.
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    6. Fang, Kai-Tai & Li, Runze, 1999. "Bayesian Statistical Inference on Elliptical Matrix Distributions," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 66-85, July.
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