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Risk Comparison of Improved Estimators in a Linear Regression Model with Multivariate t Errors under Balanced Loss Function

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  • Guikai Hu
  • Qingguo Li
  • Shenghua Yu

Abstract

Under a balanced loss function, we derive the explicit formulae of the risk of the Stein‐rule (SR) estimator, the positive‐part Stein‐rule (PSR) estimator, the feasible minimum mean squared error (FMMSE) estimator, and the adjusted feasible minimum mean squared error (AFMMSE) estimator in a linear regression model with multivariate t errors. The results show that the PSR estimator dominates the SR estimator under the balanced loss and multivariate t errors. Also, our numerical results show that these estimators dominate the ordinary least squares (OLS) estimator when the weight of precision of estimation is larger than about half, and vice versa. Furthermore, the AFMMSE estimator dominates the PSR estimator in certain occasions.

Suggested Citation

  • Guikai Hu & Qingguo Li & Shenghua Yu, 2014. "Risk Comparison of Improved Estimators in a Linear Regression Model with Multivariate t Errors under Balanced Loss Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:129205
    DOI: 10.1155/2014/129205
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    References listed on IDEAS

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    1. Akio Namba & Kazuhiro Ohtani, 2007. "Risk comparison of the Stein-rule estimator in a linear regression model with omitted relevant regressors and multivariatet errors under the Pitman nearness criterion," Statistical Papers, Springer, vol. 48(1), pages 151-162, January.
    2. Namba, Akio, 2002. "Pmse Performance Of The Biased Estimators In A Linear Regression Model When Relevant Regressors Are Omitted," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1086-1098, October.
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