Homogeneity Pursuit in Functional-Coefficient Models

Abstract

This paper studies the homogeneity of the coefficient functions in nonlinear models with functional coefficients, and identifies the semiparametric modelling structure. With initial kernel estimates of each coefficient functions, we combine the classic hierarchical clustering method and a generalised version of the information criterion to estimate the number of clusters each of which has the common functional coefficient and determine the indices within each cluster. To specify the semi-varying coefficient modelling framework, we further introduce a penalised local least squares method to determine zero coefficient, non-zero constant coefficients and functional coefficients varying with the index variable. Through the nonparametric cluster analysis and the penalised approach, the number of the unknown parametric and nonparametric components in the models can be substantially reduced and the aim of dimension reduction can be achieved. Under some regularity conditions, we establish the asymptotic properties for the proposed methods such as the consistency of the homogeneity pursuit. Some numerical studies including simulation and an empirical application are given to examine the finite sample performance of our methods.