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Comparisons of variance estimators in a misspecified linear model with elliptically contoured errors

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  • Hu, Guikai
  • Yu, Shenghua
  • Luo, Han

Abstract

In a misspecified linear regression model with elliptically contoured errors, the exact biases and risks of least squares, restricted least squares, preliminary test and Stein-type estimators of the error variance are derived. Also, we compare the risk performances of the underlying estimators and give the dominance pictures for them. It is shown that the risk of preliminary test estimator attains the smallest value if the critical value equals one. Moreover, we give a bootstrap procedure for estimating the risks of proposed estimators in order to overcome the difficulty of computing the exact risks when the sample size becomes larger.

Suggested Citation

  • Hu, Guikai & Yu, Shenghua & Luo, Han, 2015. "Comparisons of variance estimators in a misspecified linear model with elliptically contoured errors," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 266-276.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:266-276
    DOI: 10.1016/j.jmva.2014.09.012
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    References listed on IDEAS

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    1. Kazuhiro Ohtani & Alan Wan, 2009. "Comparison of the Stein and the usual estimators for the regression error variance under the Pitman nearness criterion when variables are omitted," Statistical Papers, Springer, vol. 50(1), pages 151-160, January.
    2. Ohtani, Kazuhiro, 1996. "Further improving the Stein-rule estimator using the Stein variance estimator in a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 29(3), pages 191-199, September.
    3. Namba, Akio, 2002. "Pmse Performance Of The Biased Estimators In A Linear Regression Model When Relevant Regressors Are Omitted," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1086-1098, October.
    4. Clarke, Judith A. & Giles, David E. A. & Wallace, T. Dudley, 1987. "Preliminary-Test Estimation of the Error Variance in Linear Regression," Econometric Theory, Cambridge University Press, vol. 3(02), pages 299-304, April.
    5. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    6. Arashi, M. & Tabatabaey, S.M.M., 2009. "Improved variance estimation under sub-space restriction," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1752-1760, September.
    7. Zhu, Rong & Zhou, Sherry Z.F., 2011. "Estimating the error variance after a pre-test for an interval restriction on the coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2312-2323, July.
    8. Ohtani, Kazuhiro, 2002. "Exact distribution of a pre-test estimator for regression error variance when there are omitted variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 129-140, November.
    9. M. Arashi & A. Saleh & S. Tabatabaey, 2010. "Estimation of parameters of parallelism model with elliptically distributed errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(1), pages 79-100, January.
    10. Mittelhammer, R.C., 1984. "Restricted least squares, pre-test, ols and stein rule estimators: Risk comparisons under model misspecification," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 151-164.
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