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

Record type: Article

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.

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Citation

Biedermann, Stefanie and Dette, Holger (2001) Optimal designs for testing the functional form of a regression via nonparametric estimation techniques Statistics & Probability Letters, 52, (2), pp. 215-224. (doi:10.1016/S0167-7152(00)00244-3).

More information

Published date: 1 April 2001
Additional Information: Short communication
Keywords: goodness-of-fit test, weighted least squares, optimal design, maximin optimality, D1-optimality
Organisations: Statistics

Identifiers

Local EPrints ID: 42206
URI: http://eprints.soton.ac.uk/id/eprint/42206
ISSN: 0167-7152
PURE UUID: 78001c4a-bbd4-464b-b514-7c9c4e3572c1

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Date deposited: 09 Jan 2007
Last modified: 17 Jul 2017 15:23

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Contributors

Author: Holger Dette

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