Testing heteroscedasticity in nonparametric regression

H. Dette and A. Munk

Journal of the Royal Statistical Society Series B, 1998, vol. 60, issue 4, 693-708

Abstract: The importance of being able to detect heteroscedasticity in regression is widely recognized because efficient inference for the regression function requires that heteroscedasticity is taken into account. In this paper a simple consistent test for heteroscedasticity is proposed in a nonparametric regression set‐up. The test is based on an estimator for the best L2‐approximation of the variance function by a constant. Under mild assumptions asymptotic normality of the corresponding test statistic is established even under arbitrary fixed alternatives. Confidence intervals are obtained for a corresponding measure of heteroscedasticity. The finite sample performance and robustness of these procedures are investigated in a simulation study and Box‐type corrections are suggested for small sample sizes.

Date: 1998
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