ZHU NengHui, LI Xiao, SHI YaFeng, . Weighted Profile LSDV Estimation of Fixed Effects Panel Data Partially Linear Regression Models[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 111-134.
Citation:
ZHU NengHui, LI Xiao, SHI YaFeng, . Weighted Profile LSDV Estimation of Fixed Effects Panel Data Partially Linear Regression Models[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 111-134.
ZHU NengHui, LI Xiao, SHI YaFeng, . Weighted Profile LSDV Estimation of Fixed Effects Panel Data Partially Linear Regression Models[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 111-134.
Citation:
ZHU NengHui, LI Xiao, SHI YaFeng, . Weighted Profile LSDV Estimation of Fixed Effects Panel Data Partially Linear Regression Models[J]. Chinese Journal of Applied Probability and Statistics, 2018, 34(2): 111-134.
School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024, China
School of Statistics and Management, Shanghai University of Finance and Economics Shanghai, 200433, China
School of Science, Ningbo University of Technology, Ningbo, 315211, China
Funds: The project was supported by the High-Level Personnel Fund of Xiamen University of Technology (Grant No. YKJ15031R) and the Graduate Innovation Fund of Shanghai University of Finance and Economics (Grant No. CXJJ-2013-459)
This paper concerns with the estimation of a fixed effects panel data partially linear regression model with the idiosyncratic errors being an autoregressive process. For fixed effects short time series panel data, the commonly used autoregressive error structure fitting method will not result in a consistent estimator of the autoregressive coefficients. Here we propose an alternative estimation and show that the resulting estimator of the autoregressive coefficients is consistent and this method is workable for any order autoregressive error structure. Moreover, combining the B-spline approximation, profile least squares dummy variable (PLSDV) technique and consistently estimated the autoregressive error structure, we develop a weighted PLSDV estimator for the parametric component and a weighted B-spline series (BS) estimator for the nonparametric component. The weighted PLSDV estimator is shown to be asymptotically normal and more asymptotically efficient than the one which ignores the error autoregressive structure. In addition, this paper derives the asymptotic bias of the weighted BS estimator and establish its asymptotic normality as well. Simulation studies and an example of application are conducted to illustrate the finite sample performance of the proposed procedures.