Robust Estimation and Variable Selection for Partially Linear Panel Data Models with Fixed Effects

Abstract

The paper proposes a new composite quantile regression estimation and variable selection procedures for partially linear panel data models with fixed effects. By combining forward orthogonal derivations transform with B-spline approximations, we first develop a semiparametric composite quantile regression procedure. The main advantage of the proposed method lies in its robustness compared to the least-squares-based method, especially for many non-normal errors. Under some regularity conditions, we establish the asymptotic properties of the resulting estimators. To achieve sparsity with high-dimensional covariates, we further propose adaptive Lasso penalized composite quantile regression estimation for variable selection in partially linear panel data models, and establish the oracle property under some regularity conditions. Simulation studies and a real data analysis are provided to assess the finite-sample performance of the proposed procedures.

Keywords

B-spline / Composite quantile regression / Panel data / Partially linear model / Variable selection / 62G08 / 62G20

Funding

Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0079)

Humanities and Social Sciences Program of Chongqing Education Commission(21SIGH118)

National Social Science Foundation of China(18BTJ035)

National Natural Science Foundation of China(12271046, 12131006, 11971001)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature