Corrected modified profile likelihood heteroskedasticity tests

This paper considers the issue of testing for the constancy of variances in linear regression models. We obtain a Bartlett correction to the modified profile likelihood ratio test proposed by Simonoff and Tsai (Appl. Statist. 43 (1994) 357) who have used the approach proposed by Cox and Reid (J. R. Statist. Soc. B 49 (1987) 1). Our numerical results show that the corrected test we propose outperform the original likelihood ratio test, the Bartlett-corrected likelihood ratio test, and the modified profile likelihood ratio test in small samples. The proposed test displays good finite sample behaviour at very low significance levels.