Robust estimation with exponential squared loss for partially linear panel data model with fixed effects

Abstract

In this article, a robust estimation method is proposed for a partially linear panel data model with fixed effects. We eliminate the fixed effects based on auxiliary linear regression, then approximate the unknown non parametric component with B-spline function, and obtain the robust estimators of the parametric and non parametric components by combining projection matrix with exponential squared loss function. Under some regularity conditions, the asymptotic properties of the resulting estimators are proved. Some simulation studies illustrate that the proposed method is more robust than the semiparametric least squares dummy variable estimator. The proposed procedure is illustrated by a real data application.

keyword:

• Panel data
• partially linear model
• exponential squared loss

Mathematics Subject Classification:

• 62G05
• 62G20

Additional information

Funding

Yiping Yang’s research was supported by Chongqing Natural Science Foundation (cstc2021jcyj-msxmX0079, cstc2020jcyj-msxmX0394) and Humanities and Social Sciences Program of Chongqing Education Commission (21SIGH118), Peixin Zhao’s research was supported by Chongqing Natural Science Foundation (cstc2020jcyj-msxmX0006) and the National Social Science Foundation of China (18BTJ035).