Variable selection for partially time-varying coefficient error-in-variables models

Abstract

Partially time-varying coefficient models are useful for studying the time dependent effect of variables. In this paper, we consider the variable selection for this kind of models when covariates in parametric part are observed with additive measurement errors and the sequence of observations {Zi,Xi,εi} is stationary and α-mixing. To select significant variables and enhance model predictability, a variable selection procedure with smoothly clipped absolute deviation (SCAD) penalty is developed via using profile least squares (PLS) method and local linear technique. Under some proper conditions, the oracle properties of the resulting estimator are established. Furthermore, we consider a test statistic based on penalized PLS method and prove theoretically that its limit is a weighted sum of standard chi-square random variables. Numerical examples are carried out to illustrate the finite sample performance of proposed approaches.