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Risk behavior of variance estimators in multivariate normal distribution

Author

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  • Rukhin, Andrew L.
  • Ananda, Malwane M. A.

Abstract

In this paper we consider the estimation problem of unknown variance of a multivariate normal vector under quadratic loss and entropy loss. The behavior of risk functions of the Brewster--Zidek estimator and the original Stein estimator is examined. Numerical studies show that an asymptotically inadmissible Stein estimator provides a larger degree of improvement than an admissible Brewster--Zidek estimator.

Suggested Citation

  • Rukhin, Andrew L. & Ananda, Malwane M. A., 1992. "Risk behavior of variance estimators in multivariate normal distribution," Statistics & Probability Letters, Elsevier, vol. 13(2), pages 159-166, January.
    • Handle: RePEc:eee:stapro:v:13:y:1992:i:2:p:159-166
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    Cited by:

    1. Wan, Alan T. K. & Zou, Guohua, 2003. "Optimal critical values of pre-tests when estimating the regression error variance: analytical findings under a general loss structure," Journal of Econometrics, Elsevier, vol. 114(1), pages 165-196, May.
    2. Misra, Neeraj & Singh, Harshinder & Demchuk, Eugene, 2005. "Estimation of the entropy of a multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 324-342, February.
    3. Leila Golparver & Ali Karimnezhad & Ahmad Parsian, 2013. "Optimal rules and robust Bayes estimation of a Gamma scale parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 595-622, July.
    4. Pal, Nabendu & Ling, Chiahua, 1995. "Improved minimax estimation of powers of the variance of a multivariate normal distribution under the entropy loss function," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 205-211, August.

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