Variable selection for high dimensional partially linear varying coefficient errors-in-variables models

Year 2019, Volume: 48 Issue: 1, 213 - 229, 01.02.2019

Zhaoliang Wang Liugen Xue

Abstract

In this paper,  we consider variable selection procedure for the high dimensional  partially linear varying coefficient models where  the parametric part covariates are measured with additive errors.  The penalized bias-corrected profile least squares estimators are conducted, and their asymptotic properties are also studied under some regularity conditions. The rate of convergence and the asymptotic normality of the resulting estimates are established. We further demonstrate that, with proper choices of the penalty functions and the regularization parameter, the resulting estimates perform asymptotically as well as an oracle property. Choice of smoothing parameters is also discussed. Finite sample performance of the proposed variable selection procedures is assessed by Monte Carlo simulation studies.

Keywords

High dimensionality, Measurement error, Semiparametric models, Local linear regression, Variable selection

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