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Detecting heteroscedasticity in non‐parametric regression using weighted empirical processes

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  • Justin Chown
  • Ursula U. Müller

Abstract

Heteroscedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroscedasticity for the non‐parametric regression model with multiple covariates. It is based on a suitable residual‐based empirical distribution function. The residuals are constructed by using local polynomial smoothing. Our test statistic involves a ‘detection function’ that can verify heteroscedasticity by exploiting just the independence–dependence structure between the detection function and model errors, i.e. we do not require a specific model of the variance function. The procedure is asymptotically distribution free: inferences made from it do not depend on unknown parameters. It is consistent at the parametric (root n) rate of convergence. Our results are extended to the case of missing responses and illustrated with simulations.

Suggested Citation

  • Justin Chown & Ursula U. Müller, 2018. "Detecting heteroscedasticity in non‐parametric regression using weighted empirical processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 951-974, November.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:5:p:951-974
    DOI: 10.1111/rssb.12282
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    Cited by:

    1. Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.

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