Shrinkage Estimation of the Varying Coefficient Model

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.

Number of Pages in PDF File: 35

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

JEL Classification: C52, C14

working papers series