Heteroskedasticity-Robust Inference in Linear Regressions |
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Authors: | Verônica M. C. Lima Tatiene C. Souza Francisco Cribari-Neto Gilênio B. Fernandes |
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Affiliation: | 1. Departamento de Estatística , Universidade Federal da Bahia , Salvador, BA, Brazil cadena@ufba.br;3. Departamento de Estatística , Universidade Federal da Bahia , Salvador, BA, Brazil;4. Departamento de Estatística , Universidade Federal de Pernambuco, Cidade Universitária , Recife, PE, Brazil |
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Abstract: | The assumption that all errors share the same variance (homoskedasticity) is commonly violated in empirical analyses carried out using the linear regression model. A widely adopted modeling strategy is to perform point estimation by ordinary least squares and then perform testing inference based on these point estimators and heteroskedasticity-consistent standard errors. These tests, however, tend to be size-distorted when the sample size is small and the data contain atypical observations. Furno (1996 Furno , M. ( 1996 ). Small sample behavior of a robust heteroskedasticity consistent covariance matrix estimator . Journal of Statistical Computation and Simulation 54 : 115 – 128 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggested performing point estimation using a weighted least squares mechanism in order to attenuate the effect of leverage points on the associated inference. In this article, we follow up on her proposal and define heteroskedasticity-consistent covariance matrix estimators based on residuals obtained using robust estimation methods. We report Monte Carlo simulation results (size and power) on the finite sample performance of different heteroskedasticity-robust tests. Overall, the results favor inference based on HC0 tests constructed using robust residuals. |
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Keywords: | Heteroskedasticity Leverage point Linear regression Quasi-t test Robust estimation |
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