Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects
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Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects Bang-Qiang He1
· Xing-Jian Hong2 · Guo-Liang Fan1
Received: 20 August 2017 / Revised: 10 September 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract For the partially linear errors-in-variables panel data models with fixed effects, we, in this paper, study asymptotic distributions of a corrected empirical log-likelihood ratio and maximum empirical likelihood estimator of the regression parameter. In addition, we propose penalized empirical likelihood (PEL) and variable selection procedure for the parameter with diverging numbers of parameters. By using an appropriate penalty function, we show that PEL estimators have the oracle property. Also, the PEL ratio for the vector of regression coefficients is defined and its limiting distribution is asymptotically chi-square under the null hypothesis. Moreover, empirical log-likelihood ratio for the nonparametric part is also investigated. Monte Carlo simulations are conducted to illustrate the finite sample performance of the proposed estimators. Keywords Panel data · Penalized empirical likelihood · Partially linear model · Fixed effect · Errors-in-variables
1 Introduction The analysis of panel data is the subject of one of the most active and innovative bodies of literature in econometrics. Panel data sets have various advantages over that of pure time-series or cross-sectional data sets, among which the most important one is perhaps that the panel data provide researchers a flexible way to model both heterogeneity among cross-sectional units and possible structural changes over time. Arellano (2003), Baltagi (2005) and Hsiao (2003) provided excellent overviews of statistical inference and econometric analysis of parametric panel data models. However, a misspecified parametric panel data model may result in misleading inference. Therefore, econometricians and statisticians have developed some flexible nonpara-
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Xing-Jian Hong [email protected]
1
School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China
2
School of Data Sciences, Zhejiang University of Finance & Economics, Hangzhou 310018, China
123
B.-Q. He et al.
metric and semi-parametric panel data models. For example, Su and Ullah (2007) proposed a class of two-step estimators for nonparametric panel data with random effects. Cai and Li (2008) studied dynamic nonparametric panel data models. Henderson et al. (2008) considered nonparametric panel data model with fixed effects. Rodriguez-Poo and Soberon (2014) considered varying coefficient fixed effects panel data models, established direct semiparametric estimations. Chen et al. (2013) studied partially linear single-index panel data models with fixed effects, proposed a dummy variable method to remove fixed effects and established a semi-parametric minimum average variance estimation procedure. Baltagi and Li (2002) discussed partially linear panel data models with fixed effects, developed the
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