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

✍ Scribed by Stefanie Biedermann; Holger Dette

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 126 KB
• Volume: 52
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(00)00244-3

✦ Synopsis

For the problem of checking linearity in a heteroscedastic nonparametric regression model under a ÿxed 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 deÿnition of the class of alternatives. Our results extend and put recent ÿndings of Wiens (Statist. Probab. Lett. 12 (1991) 217) in a new light, who established the maximin optimality of the uniform design for lack-of-ÿt tests in homoscedastic multiple linear regression models.