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MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated

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  • Akio Namba

Abstract

In this paper we consider a regression model and a general family of shrinkage estimators of regression coefficients. The estimation of each individual regression coefficient is important in some practical situations. Thus, we derive the formula for the mean squared error (MSE) of the general class of shrinkage estimators for each individual regression coefficient. It is shown analytically that the general family of shrinkage estimators is dominated by its positive-part variant in terms of MSE whenever there exists the positive-part variant or, in other words, the shrinkage factor can be negative for some parameter and data values. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • Akio Namba, 2015. "MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated," Statistical Papers, Springer, vol. 56(2), pages 379-390, May.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:2:p:379-390
    DOI: 10.1007/s00362-014-0586-6
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    References listed on IDEAS

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    1. Morris Goldstein & Mohsin S. Khan, 2017. "Income and Price Effects in Foreign Trade," World Scientific Book Chapters, in: TRADE CURRENCIES AND FINANCE, chapter 1, pages 3-81, World Scientific Publishing Co. Pte. Ltd..
    2. Ullah, Aman, 1974. "On the sampling distribution of improved estimators for coefficients in linear regression," Journal of Econometrics, Elsevier, vol. 2(2), pages 143-150, July.
    3. Ryo Uemukai, 2011. "Small sample properties of a ridge regression estimator when there exist omitted variables," Statistical Papers, Springer, vol. 52(4), pages 953-969, November.
    4. 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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