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Corrected Maximum Likelihood Estimators in Linear Heteroskedastic Regression Models

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  • Cordeiro, Gauss M.

Abstract

The linear heteroskedastic regression model, for which the variance of the response is given by a suitable function of a set of linear exogenous variables, is very useful in econometric applications. We derive a simple matrix formula for the n^−1 biases of the maximum likelihood estimators of the parameters in the variance of the response, where n is the sample size. These biases are easily obtained as a vector of regression coefficients in a simple weighted least squares regression. We use simulation to compare the uncorrected estimators with the bias-corrected ones to conclude the superiority of the corrected estimators over the uncorrected ones with regard to the normal approximation. The practical use of such biases is illustrated in two applications to real data sets.

Suggested Citation

  • Cordeiro, Gauss M., 2008. "Corrected Maximum Likelihood Estimators in Linear Heteroskedastic Regression Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 28(1), May.
    • Handle: RePEc:sbe:breart:v:28:y:2008:i:1:a:1515
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    1. Cordeiro, Gauss M. & Botter, Denise A., 2001. "Second-order biases of maximum likelihood estimates in overdispersed generalized linear models," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 269-280, December.
    2. Gauss Cordeiro & Lúcia Barroso, 2007. "A third-order bias corrected estimate in generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 76-89, May.
    3. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
    4. Jeffrey S. Simonoff & Chih‐Ling Tsai, 1994. "Use of Modified Profile Likelihood for Improved Tests of Constancy of Variance in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 357-370, June.
    5. Cordeiro, Gauss M. & Klein, Ruben, 1994. "Bias correction in ARMA models," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 169-176, February.
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    1. Alexandre Patriota & Artur Lemonte & Heleno Bolfarine, 2011. "Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model," Statistical Papers, Springer, vol. 52(2), pages 455-467, May.
    2. Patriota, Alexandre G. & Lemonte, Artur J., 2009. "Bias correction in a multivariate normal regression model with general parameterization," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1655-1662, August.

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