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MSE performance of the weighted average estimators consisting of shrinkage estimators

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  • Akio Namba
  • Kazuhiro Ohtani

Abstract

In this paper, we consider a regression model and propose estimators which are the weighted averages of two estimators among three estimators; the Stein-rule (SR), the minimum mean squared error (MMSE), and the adjusted minimum mean-squared error (AMMSE) estimators. It is shown that one of the proposed estimators has smaller mean-squared error (MSE) than the positive-part Stein-rule (PSR) estimator over a moderate region of parameter space when the number of the regression coefficients is small (i.e., 3), and its MSE performance is comparable to the PSR estimator even when the number of the regression coefficients is not so small.

Suggested Citation

  • Akio Namba & Kazuhiro Ohtani, 2018. "MSE performance of the weighted average estimators consisting of shrinkage estimators," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1204-1214, March.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:5:p:1204-1214
    DOI: 10.1080/03610926.2017.1316860
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    1. Brownstone, David, 1990. "Bootstrapping improved estimators for linear regression models," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 171-187.
    2. Ohtani, Kazuhiro, 1999. "MSE performance of a heterogeneous pre-test estimator," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 65-71, January.
    3. Chi, Xie Wen & Judge, George, 1985. "On assessing the precision of Stein's estimator," Economics Letters, Elsevier, vol. 18(2-3), pages 143-148.
    4. Yi, Gang, 1991. "Estimating the variability of the Stein estimator by bootstrap," Economics Letters, Elsevier, vol. 37(3), pages 293-298, November.
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