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

Abstract

a b s t r a c tThis paper focuses on the variable selections for semiparametric varying coefficient partially linear models when the covariates in the parametric and nonparametric components are all measured with errors. A bias-corrected variable selection procedure is proposed by combining basis function approximations with shrinkage estimations. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the regularized estimators are established. A simulation study and a real data application are undertaken to evaluate the finite sample performance of the proposed method.

Variable selection for joint mean and dispersion models of the inverse Gaussian distribution

“…And as in Li and Liang (2008), Zhao and Xue (2010) the performance of estimatorsβ andγ will be assessed by using the generalized mean square error (GMSE), defined as…”

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

“…As a natural extension of [5], which used marginal model for longitudinal data analysis, a random effect method is developed when considering within-subject correlation and further shrinkage estimation. In the literatures in longitudinal data study, random effect method has received relatively enough attention.…”

“…See, for example, [10]- [13]. Also, some extensions of the variable selection under the regularization framework to varying coefficient models include, [5] [14]- [16]. In this article, the variable selection problem for PLVC model with random effect is investigated.…”

Functional index coefficient models with variable selection

“…The shrinkage method has been successfully extended to semiparametric models; for example, variable selection in partially linear models in Liang and Li (2009), partially linear models in longitudinal data in Fan and Li (2004), single-index models in Kong and Xia (2007), semiparametric regression models in Brent et al (2008) and Li and Liang (2008), varying coefficient partially linear models with errors-in-variables in Zhao and Xue (2010), and partially linear single-index models in Liang et al (2010), and the references therein.…”