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 xed design assumption we study maximin designs which maximize the minimum power of a nonparametric test over a broad class of alternatives from the as sumed linear regression model It is demonstrated that the optimal design depends sensi tively on the used estimation technique i e weighted or ordinary least squares and on an inner product used in the de niton of the class of alternatives Our results extend and put recent ndings of Wiens in a new light who established the maximin optimality of the uniform design for lack of t tests in homoscedastic multiple linear regression models AMS Subject classi cations Primary K G Secondary G J