Variable selection for longitudinal varying coefficient errors-in-variables models

Abstract

In this paper, we investigate the variable selection for varying coefficient errors-in-variables (EV) models with longitudinal data when some covariates are measured with additive errors. A variable selection method based on bias-corrected penalized quadratic inference function (pQIF) is proposed by combining the basis function approximation to coefficient functions and bias-corrected quadratic inference function (QIF) with shrinkage estimations. The proposed method can handle the measurement errors of covariates and within-subject correlation, estimate and select non-zero nonparametric coefficient functions. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection method and the sparsity properties of the regularized estimators. The finite sample performance of the proposed method is assessed by simulation studies. The utility of the method is further demonstrated via a real data analysis.