Varying-Coefficient Models: New Models, Inference Procedures, and Applications

Motivated by an empirical analysis of a data set collected in the field of ecology, we proposed nonlinear varying-coefficient models, a new class of varying-coefficient models. We further propose an estimation procedure for the nonlinear varying-coefficient models by using local linear regression,study the asymptotic properties of the proposed procedures, and establish the asymptotic normality of the resulting estimate. We also extend generalized likelihood ratio-type test (Fan, Zhang and Zhang, 2001) for the nonlinear varying-coefficient models for testing whether the coefficients really depend on a covariate. To assess the finite sample performance of the proposed procedures, we conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the procedures. By Monte Carlo simulation, we empirically show the Wilks' phenomenon valid for the proposed generalized likelihood ratio test. That is, we empirically show that the asymptotic null distribution has a chi-square distribution with degrees of freedom which do not depend on the unknown parameters presented in the model under the null hypothesis. As new applications of varying coefficient models, we applied some existing procedures for some financial data sets. We demonstrated the varying-coefficient models are superior to an ordinary linear regression model, the commonlyused model in finance research. We also apply the proposed estimation and inference procedure on the empirical study in the field of ecology.