Detecting heteroscedasticity in non-parametric regression using weighted empirical processes

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2018 · Volume 80 · Issue 5

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 (rootn) rate of convergence. Our results are extended to the case of missing responses and illustrated with simulations.

Keywords

Heteroscedastic non-parametric regression, Local polynomial smoother, Missingness at random, Transfer principle, Weighted empirical process

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