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A New Test of Linear Hypotheses in OLS Regression Under Heteroscedasticity of Unknown Form

A New Test of Linear Hypotheses in OLS Regression Under Heteroscedasticity of Unknown Form When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM) estimator. However, many HCCM estimators do not perform well when the sample size is small or when there exist points of high leverage in the design matrix. Prompted by a connection between MacKinnon and White’s HC2 HCCM estimator and the heterogeneous-variance two-sample t statistic, the authors provide a new statistic for testing linear hypotheses in an OLS regression model that does not assume homoscedasticity. The authors report simulation results showing that their new test maintains better Type I error rate control than existing methods in both the presence and absence of heteroscedasticity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Educational and Behavioral Statistics SAGE

A New Test of Linear Hypotheses in OLS Regression Under Heteroscedasticity of Unknown Form

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References (42)

Publisher
SAGE
Copyright
Copyright © by SAGE Publications
ISSN
1076-9986
eISSN
1935-1054
DOI
10.3102/1076998607302628
Publisher site
See Article on Publisher Site

Abstract

When the errors in an ordinary least squares (OLS) regression model are heteroscedastic, hypothesis tests involving the regression coefficients can have Type I error rates that are far from the nominal significance level. Asymptotically, this problem can be rectified with the use of a heteroscedasticity-consistent covariance matrix (HCCM) estimator. However, many HCCM estimators do not perform well when the sample size is small or when there exist points of high leverage in the design matrix. Prompted by a connection between MacKinnon and White’s HC2 HCCM estimator and the heterogeneous-variance two-sample t statistic, the authors provide a new statistic for testing linear hypotheses in an OLS regression model that does not assume homoscedasticity. The authors report simulation results showing that their new test maintains better Type I error rate control than existing methods in both the presence and absence of heteroscedasticity.

Journal

Journal of Educational and Behavioral StatisticsSAGE

Published: Mar 1, 2008

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