Statistica Sinica 22 (2012), 575-599

doi:http://dx.doi.org/10.5705/ss.2010.105

ADAPTIVE SEMI-VARYING COEFFICIENT MODEL

SELECTION

Tao Hu$^{1,2}$ and Yingcun Xia$^3$

$^1$Guizhou College of Finance and Economics, $^2$Capital Normal University

and $^3$National University of Singapore

Abstract: Identification of constant coefficients in a semi-varying coefficient model is an important issue (Zhang et al (2002)). We propose a novel method for this by combining local polynomial smoothing (Fan and Zhang (1999)) with shrinkage estimation (Tibshirani (1996)). Unlike the stepwise procedure (Xia et al (2004)), our method can identify the constant coefficients and estimate the model simultaneously. By imposing the adaptive LASSO penalty and starting with the Nadaraya-Watson estimator, the method can identify the constant coefficients and varying coefficients consistently, and estimate the model with oracle efficiency (Fan and Li (2001)).

Key words and phrases: BIC, kernel smoothing, LASSO, model selection, oracle property, SCAD, semi-varying coefficient model.