Optimal minimax rates for nonparametric specification testing in regression models

摘要

In the context of testing th especification of a nonlinear parametric regreesion function we adopt a nonparametric minimax approach to determine the maximum rate at which a set of smooth altrnatives can approach the null hypothesis while ensuring htat a stest can uniformaly detect any alternative in this set with some predetermined power Weshow that a smooth nonparametric test has optimal asymptotic minimax properties for regular alternatives As as by-product we obtain the rate of the smoothing prameter that ensures rate-optimality of th test We show that in contrast a class of nonsmooth tests which includes the integrated conditional moment test of Bierens (1982 Journal of Econometrics 20,105-134) has suboptimal asymptotic minimax properties.