On a Principal Varying Coefficient Model

Abstract

We propose a novel varying coefficient model, called principal varying coefficient model (PVCM), by characterizing the varying coefficients through linear combinations of a few principal functions. Compared with the conventional varying coefficient model (VCM; Chen and Tsay, 1993; Hastie and Tibshirani, 1993), PVCM reduces the actual number of nonparametric functions, and thus has better estimation efficiency. Compared with the semi-varying coefficient model (SVCM; Zhang et al, 2002; Fan and Huang, 2005), PVCM is more flexible but with the same estimation efficiency when the number of principal functions in PVCM and the number of varying coefficients in SVCM are the same. Model estimation and identification are investigated, and the better estimation efficiency is justified theoretically. Incorporating the estimation with the L1-penalty, variables in the linear combinations can be selected automatically and hence the estimation efficiency can be further improved. Numerical experiments suggest that the model together with the estimation method are useful even when the number of covariates is large.

Keywords: local linear estimator, L1-penalty, principal function, profile least-squares estimation, semi-varying coefficient model, varying coefficient model

JEL Classification: C10, C13, C14