Variable Selection in Nonparametric Statistics

• Activity Number: 303
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Adriano Zanin Zambom*+ and Michael G. Akritas
• Companies: Penn State University and Penn State University
• Keywords: nonparametric regression ; ANOVA ; variable selection ; reduce dimension ; asymptotic normality ; hypothesis test

Abstract

In nonparametric regression where we do not want to make restrictive assumptions about the mean function, reducing the dimension of the explanatory variable leads to easier interpretation of the model and better estimates. In this context, we propose a procedure for testing that the nonparametric regression function depends only on a subset of the available covariates, when the mean regression function is not necessarily additive. This hypothesis test is based on recent developments of the asymptotic theory of ANOVA when the number of factor levels goes to infinity. The asymptotic distribution of the test statistic under the null hypothesis is proven to be normal. Simulation results show that this test has better power than previous methods by Lavergne 2000 and Fan and Li 1996, both under linear and nonlinear alternatives.