Events and Seminars : 2012 Seminars

A Nonparametric R2 Test for the Presence of Relevant Variables

Feng Yao
Professor, Department of Economics, West Virginia University

October 19, 2012

We propose a nonparametric test for the presence of relevant variables based on a measure of nonparametric goodness-of-fit (R2) in a regression model. It does not require correct specifications of the conditional mean function, thus is able to detect presence of relevant variables of unknown form. Our test statistic is based on an appropriately centered and standardized nonparametric R2 estimator, which is obtained from a local linear regression. We establish the asymptotic normality of the test statistic under the null hypothesis that relevant variables are not present and a sequence of Pitman local alternatives.

We also prove the consistency of the test, and show that the Wild bootstrap/bootstrap method can be used to approximate the null distribution of the test statistic. Under the alternative hypothesis, we establish the asymptotic normality of the nonparametric R2 estimator at rate pn, which facilitates inference using the nonparametric measure of goodness-of-fit. We illustrate the finite sample performance of the test statistics with a Monte Carlo study and the tests perform well relative to other alternatives.