Testing in nonparametric varying coefficient 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 mul- tivariate regression model. We propose a test statistic and derive its asymptotic null and alternative distributions. We analyze the asymptotic power of the test in shrinking neighborhoods of the null hypothesis and show that the test is asymp- totically optimal. These results are derived under the fairly general condition of absolute regularity (β-mixing) for the predictor variables. We give numerical re- sults that support the theory. 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 individual body fat values well.