Müller, Ursula U.
|Title:||Detecting heteroskedasticity in nonparametric regression using weighted empirical processes|
|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
missing at random
local polynomial smoother
|Subject Headings (RSWK):||Heteroskedastizität|
|Appears in Collections:||Sonderforschungsbereich (SFB) 823|
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|DP_5016_SFB823_Chown_Müller.pdf||DNB||419.34 kB||Adobe PDF||View/Open|
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