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MSE Performance of the Weighted Average Estimators Consisting of Shrinkage Estimators

Author

Listed:
  • Akio Namba

    (Graduate School of Economics, Kobe University)

  • Kazuhiro Ohtani

    (Graduate School of Economics, Kobe University)

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), minimum mean squared error (MMSE) and the adjusted minimum mean squared error (AMMSE) estimators. We derive the formula for the mean squared error (MSE) of the proposed estimators. It is shown by numerical evaluations 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). Also, its MSE performance is comparable to the PSR estimator even when the number of the regression coefficient is not so small.

Suggested Citation

  • Akio Namba & Kazuhiro Ohtani, 2015. "MSE Performance of the Weighted Average Estimators Consisting of Shrinkage Estimators," Discussion Papers 1513, Graduate School of Economics, Kobe University.
    • Handle: RePEc:koe:wpaper:1513
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    References listed on IDEAS

    as
    1. Brownstone, David, 1990. "Bootstrapping improved estimators for linear regression models," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 171-187.
    2. Yi, Gang, 1991. "Estimating the variability of the Stein estimator by bootstrap," Economics Letters, Elsevier, vol. 37(3), pages 293-298, November.
    3. Ohtani, Kazuhiro, 1999. "MSE performance of a heterogeneous pre-test estimator," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 65-71, January.
    4. Chi, Xie Wen & Judge, George, 1985. "On assessing the precision of Stein's estimator," Economics Letters, Elsevier, vol. 18(2-3), pages 143-148.
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