Statistical inference for fixed-effects partially linear regression models with errors in variables

Abstract

Fixed-effects partially linear regression models are useful tools to analyze data from economic, genetic and other fields. In this paper, we consider estimation and inference procedures when some of the covariates are measured with errors. The previously proposed estimations, including difference-based series estimation (Baltagi and Li in Ann Econ Finan 3:103--116, 2002) and profile least squares estimation (Fan et al. in J Am Stat Assoc 100:781--813, 2005) are no longer consistent because of the attenuation. We propose a new estimation by taking the measurement errors into account. Our proposed estimators are shown to be consistent and asymptotically normal. Consistent estimations of the error variance are also developed. In addition, we propose a variable-selection procedure to variable selection in the parametric part. The procedure is an extension of the nonconcave penalized likelihood (Fan and Li in J Am Stat Assoc 85:1348--1360, 2001), which simultaneously selects the important variables and estimates the unknown parameters. The resulting estimate is shown to possess an oracle property. Extensive simulation studies are conducted to illustrate the finite sample performance of the proposed procedures.