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Bootstrapping the Stein-Rule Estimators

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  • Akio Namba

    (Kobe University)

Abstract

In this paper we consider the Stein-rule estimator and the positive-part Stein-rule estimator for the mean of a multivariate normal distribution and analyze the validity of the bootstrap methods for these estimators. We show that the conventional bootstrap is not always consistent and propose an alternative bootstrap method which is consistent when the conventional bootstrap is inconsistent. We also show the consistency of the m out of n bootstrap. Moreover, we propose an consistent bootstrap method based on a pre-test. Our simulation results show the validity of the proposed bootstrap in various setups.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jqecon:v:19:y:2021:i:1:d:10.1007_s40953-021-00269-5
    DOI: 10.1007/s40953-021-00269-5
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    References listed on IDEAS

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    6. Vinod, H. D., 1995. "Double bootstrap for shrinkage estimators," Journal of Econometrics, Elsevier, vol. 68(2), pages 287-302, August.
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    12. 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.
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    Cited by:

    1. Yong Bao & Aman Ullah, 2021. "The Special Issue in Honor of Anirudh Lal Nagar: An Introduction," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 1-8, December.

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    More about this item

    Keywords

    Stein-rule estimator; m out of n bootstrap; Centered bootstrap; Pre-test bootstrap;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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