Equivalent Nonparametric Regression Tests Based on Spline and Local Polynomial Smoothers

• Activity Number: 149
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Chunming Zhang*+
• Affiliation(s): University of Wisconsin, Madison
• Keywords: nonparametric goodness-of-fit test ; local polynomial regression ; power ; smoothing spline ; smoothing parameter ; Wilks theorem

Abstract

It is well known that a smoothing spline estimate of regression functions is asymptotically equivalent to a kernel-type estimate. However, little information has been available about whether nonparametric diagnostic tests of the regression functions, based on smoothing spline and kernel-type methods, are equivalent. In this paper, we consider the ''generalized likelihood ratio" test statistics constructed from using both smoothing spline and kernel-type smoothers, and derive explicitly the equivalent forms of the asymptotic distributions. Furthermore, we derive the optimal rate of smoothing parameter in the resulting spline-based test and suggest the choice of kernel function for the kernel-based test. Their relative powers are then examined by large-sample analysis and simulation.