The Glejser test is affected by a non-vanishing estimation effect in the presence of skewed error distributions, since this test over-rejects the true null hypothesis of homoskedasticity. The paper shows that this is not the only case of over-rejection, and that such effect occurs with contaminated errors as well. This implies that a correction which is appropriate to cope with skewness is inappropriate when there is contamination in the errors. In order to deal with this issue, the use of residuals estimated by the conditional median regression (least absolute deviations or LAD) is here considered. The paper shows why LAD is effective against both skewness and contamination, the motivation is linked to the coincidence between the LAD normal equation and one term of the Taylor expansion approximating the Glejser test function. The effectiveness of LAD is confirmed by a small simulation experiment here implemented. 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.

The Glejser test and the median regression

FURNO, Marilena
2005

Abstract

The Glejser test is affected by a non-vanishing estimation effect in the presence of skewed error distributions, since this test over-rejects the true null hypothesis of homoskedasticity. The paper shows that this is not the only case of over-rejection, and that such effect occurs with contaminated errors as well. This implies that a correction which is appropriate to cope with skewness is inappropriate when there is contamination in the errors. In order to deal with this issue, the use of residuals estimated by the conditional median regression (least absolute deviations or LAD) is here considered. The paper shows why LAD is effective against both skewness and contamination, the motivation is linked to the coincidence between the LAD normal equation and one term of the Taylor expansion approximating the Glejser test function. The effectiveness of LAD is confirmed by a small simulation experiment here implemented. 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11580/9192
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