Authors: Chown, Justin
Müller, Ursula U.
Title: Detecting heteroskedasticity in nonparametric regression using weighted empirical processes
Language (ISO): en
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.
Subject Headings: heteroskedastic nonparametric regression
weighted empirical process
transfer principle
missing at random
local polynomial smoother
Subject Headings (RSWK): Heteroskedastizität
Nichtparametrische Regression
Statistischer Test
Issue Date: 2016
Appears in Collections:Sonderforschungsbereich (SFB) 823

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