Testing for Varying Coefficient in Additive Models

Abstract

We consider the problem of testing for a general parametric form against a nonparametric alternative for a coefficient function in a varying coefficient multivariate regression model. We propose a statistical test for the coefficients in the varying coefficient model. The test statistic is based on a difference of nonparametric estimator and the closest parametric estimator. Here we adopt the nonparametric estimator based on the marginal integration method and the smooth backfitting method. We derive its asymptotic null and alternative distributions. We analyze the asymptotic power of the test in shrinking neighborhoods of the null hypothesis. The wild bootstrap is adapted to apply the distribution of the test statistics into real data. Their finite sample properties are also compared through simulation experiments. We also illustrate usefulness of the method through an application to a body fat dataset where we build a simple, yet accurate, model that predicts well individual body fat values.