Shrinkage Estimation of the Varying Coefficient Model

35 Pages Posted: 23 Nov 2008 Last revised: 30 Nov 2008

See all articles by Hansheng Wang

Hansheng Wang

Peking University - Guanghua School of Management

Yingcun Xia

National University of Singapore (NUS)

Date Written: October 29, 2008

Abstract

The varying coefficient model is a useful extension of the linear regression model. Nevertheless, how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood. To solve the problem, we propose here a novel method, which combines the ideas of the local polynomial smoothing (Fan and Zhang, 1999) and the shrinkage estimation (Tibshirani, 1996, LASSO). The new method can do nonparametric estimation and variable selection simultaneously. With a local constant estimator and the adaptive LASSO penalty, the new method can identify the true model consistently, and that the resulting estimator can be as efficient as the oracle estimator (Fan and Li, 2001). Numerical studies clearly confirm our theories. Extension to other shrinkage methods (e.g., the SCAD) and other smoothing methods (Zhang and Lin, 2003) is straightforward.

Keywords: BIC, LASSO, Kernel Smoothing, Oracle Property, SCAD, Variable Selection, Varying Coefficient Model

JEL Classification: C52, C14

Suggested Citation

Wang, Hansheng and Xia, Yingcun, Shrinkage Estimation of the Varying Coefficient Model (October 29, 2008). Available at SSRN: https://ssrn.com/abstract=1305588 or http://dx.doi.org/10.2139/ssrn.1305588

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Yingcun Xia

National University of Singapore (NUS) ( email )

Bukit Timah Road 469 G
Singapore, 117591
Singapore

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