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Pmse Performance Of The Biased Estimators In A Linear Regression Model When Relevant Regressors Are Omitted

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  • Namba, Akio

Abstract

In this paper, we consider a linear regression model when relevant regressors are omitted. We derive the explicit formulae for the predictive mean squared errors (PMSEs) of the Stein-rule (SR) estimator, the positive-part Stein-rule (PSR) estimator, the minimum mean squared error (MMSE) estimator, and the adjusted minimum mean squared error (AMMSE) estimator. It is shown analytically that the PSR estimator dominates the SR estimator in terms of PMSE even when there are omitted relevant regressors. Also, our numerical results show that the PSR estimator and the AMMSE estimator have much smaller PMSEs than the ordinary least squares estimator even when the relevant regressors are omitted.

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  • 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.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:05:p:1086-1098_18
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    Cited by:

    1. Zhang, Xinyu & Chen, Ti & Wan, Alan T.K. & Zou, Guohua, 2009. "Robustness of Stein-type estimators under a non-scalar error covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2376-2388, November.
    2. Hu, Guikai & Yu, Shenghua & Luo, Han, 2015. "Comparisons of variance estimators in a misspecified linear model with elliptically contoured errors," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 266-276.
    3. 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.
    4. Namba, Akio & Ohtani, Kazuhiro, 2006. "PMSE performance of the Stein-rule and positive-part Stein-rule estimators in a regression model with or without proxy variables," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 898-906, May.
    5. Namba, Akio, 2003. "PMSE dominance of the positive-part shrinkage estimator in a regression model when relevant regressors are omitted," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 375-385, July.

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