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Biometrika 2000 87(4):907-918; doi:10.1093/biomet/87.4.907
© 2000 by Biometrika Trust
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Improved heteroscedasticity-consistent covariance matrix estimators

Francisco Cribari-Neto, Silvia L. P. Ferrari and Gauss M. Cordeiro

Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Recife/PE, 50740-540, Brazil cribari@de.ufpe.br Departamento de Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo/SP, 05315-970, Brazil sferrari@ime.usp.br Departamento de Estatística, Universidade Federal da Bahia, Ondina, Salvador/BA, 40170-110, Brazil gauss@ufba.br

The heteroscedasticity-consistent covariance matrix estimator proposed by White (1980) is commonly used in practical applications and is implemented into a number of pieces of statistical software. However, although consistent, it can display substantial bias in small to moderately large samples, as shown by Monte Carlo simulations elsewhere. This paper defines modified White estimators which are approximately bias-free. Numerical results show that the modified estimators display much smaller bias than White's estimator in small samples. We also show that the bias correction leads to some variance inflation. In hypothesis testing based on heteroscedasticity-consistent covariance matrix estimators, numerical results suggest that tests based on the proposed bias-corrected estimators typically display smaller size distortions.

Key Words: Bias correction; Covariance matrix estimation; Heteroscedasticity; Linear regression; White's estimator.


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