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Estimation of selected parameters

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  • Pan, Jia-Chiun
  • Huang, Yufen
  • Hwang, J.T. Gene

Abstract

Modern statistical problems often involve selection of populations (or genes for example) using the observations. After selecting the populations, it is important to estimate the corresponding parameters. These quantities are called the selected parameters. Using traditional estimators, such as maximum likelihood (ML) estimator, which ignores the selection can result in a large bias. It is, however, known that the Bayes estimator that ignores the selection still works well under the assumed prior distribution. But, when the prior distribution used to derive the Bayes estimator is very different from the “true” prior, the Bayes estimator can fail. The paper aims to construct estimators for the selected parameters which are robust to prior distributions. A generalization of the multiple-shrinkage Stein type estimator proposed by George (1986a, 1986b) is proposed and is shown to have a small selection bias for estimating the selected means and have an attractive small expected mean squared error. With respect to these two criteria, the proposed estimator is generally better than ML estimator, Lindley–James–Stein (LJS) estimator and Efron–Tweedie (Efron, 2011) estimator.

Suggested Citation

  • Pan, Jia-Chiun & Huang, Yufen & Hwang, J.T. Gene, 2017. "Estimation of selected parameters," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 45-63.
    • Handle: RePEc:eee:csdana:v:109:y:2017:i:c:p:45-63
    DOI: 10.1016/j.csda.2016.11.001
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    References listed on IDEAS

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    1. Bradley Efron, 2014. "Estimation and Accuracy After Model Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 991-1007, September.
    2. J. T. Gene Hwang & Zhigen Zhao, 2013. "Empirical Bayes Confidence Intervals for Selected Parameters in High-Dimensional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 607-618, June.
    3. Zhigen Zhao & J. T. Gene Hwang, 2012. "Empirical Bayes false coverage rate controlling confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(5), pages 871-891, November.
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    Cited by:

    1. Yeil Kwon & Zhigen Zhao, 2023. "On F-modelling-based empirical Bayes estimation of variances," Biometrika, Biometrika Trust, vol. 110(1), pages 69-81.

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