Optimal designs for testing the functional form of a regression via nonparametric estimation techniques
Optimal designs for testing the functional form of a regression via nonparametric estimation techniques
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.
goodness-of-fit test, weighted least squares, optimal design, maximin optimality, D1-optimality
215-224
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
1 April 2001
Biedermann, Stefanie
fe3027d2-13c3-4d9a-bfef-bcc7c6415039
Dette, Holger
8c7b1c2e-3adc-45df-acfc-9e76509a228e
Biedermann, Stefanie and Dette, Holger
(2001)
Optimal designs for testing the functional form of a regression via nonparametric estimation techniques.
Statistics and Probability Letters, 52 (2), .
(doi:10.1016/S0167-7152(00)00244-3).
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.
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Published date: 1 April 2001
Additional Information:
Short communication
Keywords:
goodness-of-fit test, weighted least squares, optimal design, maximin optimality, D1-optimality
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Statistics
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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: 16 Mar 2024 03:51
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Author:
Holger Dette
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