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A Comparison of the Stein-Rule and Positive-Part Stein-Rule Estimators in a Misspecified Linear Regression Model

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  • Ohtani, Kazuhiro

Abstract

In this paper, we examine the performance of the predictive risk of the Steinrule (SR) and positive-part Stein-rule (PSR) estimators when relevant regressors are omitted in the specified model. The exact formula of the predictive risk of the PSR estimator is derived, and the sufficient condition for the PSR estimator to dominate the SR estimator under a specification error is given. It is shown by numerical computation that the PSR estimator seems to be the best choice among the OLS, SR, and PSR estimators even when there are omitted variables.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:04:p:668-679_00
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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. Ohtani, Kazuhiro, 2002. "Exact distribution of a pre-test estimator for regression error variance when there are omitted variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 129-140, November.
    3. 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.
    4. Kazuhiro Ohtani, 1998. "An MSE comparison of the restricted Stein-rule and minimum mean squared error estimators in regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 361-376, December.
    5. A. Saleh & B. Kibria, 2013. "Improved ridge regression estimators for the logistic regression model," Computational Statistics, Springer, vol. 28(6), pages 2519-2558, December.
    6. 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.
    7. Akio Namba, 2021. "Bootstrapping the Stein-Rule Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 219-237, December.
    8. 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.
    9. Ohtani, Kazuhiro, 1996. "Further improving the Stein-rule estimator using the Stein variance estimator in a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 191-199, September.
    10. 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.
    11. A. Saleh & B. Golam Kibria, 2011. "On some ridge regression estimators: a nonparametric approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 819-851.
    12. Ohtani, Kazuhiro & Kozumi, Hideo, 1996. "The exact general formulae for the moments and the MSE dominance of the Stein-rule and positive-part Stein-rule estimators," Journal of Econometrics, Elsevier, vol. 74(2), pages 273-287, October.

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