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

Biedermann, Stefanie and Dette, Holger (1970) Optimal designs for testing the functional form of a regression via nonparametric estimation techniques. Statistics & Probability Letters, 52, (2), 215-224. (doi:10.1016/S0167-7152(00)00244-3).

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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0167-7152(00)00244-3
Additional Information: Short communication
ISSNs: 0167-7152 (print)
Related URLs:
Keywords: goodness-of-fit test, weighted least squares, optimal design, maximin optimality, D1-optimality
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 42206
Accepted Date and Publication Date:
1 January 1970UNSPECIFIED
Date Deposited: 09 Jan 2007
Last Modified: 31 Mar 2016 12:14
URI: http://eprints.soton.ac.uk/id/eprint/42206

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