Optimal designs for testing the functional form of a regression via nonparametric estimation techniques

Stefanie Biedermann and Holger Dette

No 2000,41, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

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 finndings 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.

Keywords: goodness-of-fit test; weighted least squares; optimal design; maximin optimality; D1-optimality (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200041

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