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Unbiased estimation of the MSE matrices of improved estimators in linear regression

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  • Alan Wan
  • Anoop Chaturvedi
  • Guohuazou Zou

Abstract

Stein-rule and other improved estimators have scarcely been used in empirical work. One major reason is that it is not easy to obtain precision measures for these estimators. In this paper, we derive unbiased estimators for both the mean squared error (MSE) and the scaled MSE matrices of a class of Stein-type estimators. Our derivation provides the basis for measuring the estimators' precision and constructing confidence bands. Comparisons are made between these MSE estimators and the least squares covariance estimator. For illustration, the methodology is applied to data on energy consumption.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Journal of Applied Statistics.

Volume (Year): 30 (2003)
Issue (Month): 2 ()
Pages: 173-189

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Handle: RePEc:taf:japsta:v:30:y:2003:i:2:p:173-189

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Cited by:
  1. Chaturvedi, Anoop & Gupta, Suchita & Bhatti, M. Ishaq, 2012. "Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 140-158, February.
  2. Ahmed, S. Ejaz & Nicol, Christopher J., 2012. "An application of shrinkage estimation to the nonlinear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3309-3321.
  3. Zhang, Xinyu & Chen, Ti & Wan, Alan T.K. & Zou, Guohua, 2009. "Robustness of Stein-type estimators under a non-scalar error covariance structure," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2376-2388, November.
  4. Helen X. H. Bao & Alan T. K. Wan, 2007. "Improved Estimators of Hedonic Housing Price Models," Journal of Real Estate Research, American Real Estate Society, vol. 29(3), pages 267-302.

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