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Testing heteroscedasticity in nonparametric regression

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  • H. Dette
  • A. Munk

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.

Suggested Citation

  • H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:4:p:693-708
    DOI: 10.1111/1467-9868.00149
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