Estimation and variable selection for partially linear additive models with measurement errors

Rui Li, Shuchuan Mu and Ruili Hao

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 6, 1416-1445

Abstract: This article is concerned with statistical inference of partially linear additive regression models where the covariates in parametric component are measured with errors. Using polynomial spline approximations, we propose bias-corrected least squares estimators for parameters and establish the asymptotic normality, and show that the estimators of unknown functions achieve optimal nonparametric convergence rate. Moreover, we propose a variable selection procedure to identify significant regressors and derive the oracle property of penalized estimators. Finally, we propose two-stage local polynomial estimation for additive functions and show the corresponding asymptotical normality. Monte carlo studies and real data analysis illustrate the performance of our approaches.

Date: 2021
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DOI: 10.1080/03610926.2019.1651858

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