Statistica Sinica 21 (2011), 749-778

TESTING IN NONPARAMETRIC VARYING COEFFICIENT

ADDITIVE MODELS

Byeong U. Park$^1$, Jun H. Hwang$^2$ and Min S. Park$^1$

$^1$Seoul National University and $^2$Hyundai Capital

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 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 asymptotically optimal. These results are derived under the fairly general condition of absolute regularity ($\beta$-mixing) for the predictor variables. We give numerical results 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.

Key words and phrases: Backfitting, local polynomial fitting, marginal integration, varying coefficient models, wild bootstrap.