Sankhya: The Indian Journal of Statistics

2005, Volume 67, Pt. 2, 335--358

The Glejser Test and the Median Regression

By

Marilena Furno, Universit\'a di Cassino, Italy

SUMMARY. The Glejser test is affected by a non-vanishing estimation effect in the presence of skewness. We show that such effect occurs with contaminated errors as well, and that skewness correction is inappropriate when there is contamination. We consider the use of residuals estimated with conditional median regression (least absolute deviations or LAD) and discuss why LAD is effective against both skewness and contamination. The effectiveness of LAD is confirmed by simulations. With contaminated errors, both standard and skewness corrected Glejser tests perform poorly when based on least squares residuals. However, they perform very well when implemented using LAD residuals. The latter turns out to be a good alternative to bootstrap methods, which is generally used to solve the discrepancy between asymptotic and finite sample behaviour of a test.

AMS (1991) subject classification. Primary 62F03, 62J05; Secondary 62P20.

Key words and phrases. Glejser test, skewness, influence function, quantile regression.

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