Detecting heteroskedasticity in nonparametric regression using weighted empirical processes
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Date
2016
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Abstract
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are
not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression
model with multiple covariates. It is based on a suitable residual-based empirical
distribution function. The residuals are constructed using local polynomial smoothing. Our
test statistic involves a "detection function" that can verify heteroskedasticity 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.
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Keywords
heteroskedastic nonparametric regression, weighted empirical process, transfer principle, missing at random, local polynomial smoother