Authors: Biedermann, Stefanie
Dette, Holger
Title: Optimal designs for testing the functional form of a regression via nonparametric estimation techniques
Language (ISO): en
Abstract: For the problem of checking linearity in a heteroscedastic nonparametric regression model under a fixed design assumption we study maximin designs which maximize the minimum power of a nonparametric test over a broad class of alternatives from the assumed linear regression model. It is demonstrated that the optimal design depends sensitively on the used estimation technique (i.e. weighted or ordinary least squares) and on an inner product used in the definiton of the class of alternatives. Our results extend and put recent findings of Wiens (1991) in a new light, who established the maximin optimality of the uniform design for lack-of-fit tests in homoscedastic multiple linear regression models.
Subject Headings: D1 -optimality
goodness-of-fit test
maximin optimality
optimal design
weighted least squares
Issue Date: 2000
Provenance: Universitätsbibliothek Dortmund
Appears in Collections:Sonderforschungsbereich (SFB) 475

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