In this paper, semiparametric estimation of a regression function in the third order partially linear autoregressive model with first order autoregressive errors is mainly studied. We suppose that the regression function has a parametric framework, and use the conditional least squares method to obtain the parameter estimators. Then semiparametric estimators of the regression function can be given by combining with the nonparametric kernel function adjustment. Furthermore, under certain conditions, the consistency of the estimators is proved. Finally, simulation research is presented to evaluate the
effectiveness of the proposed method.
The project was supported by the National Natural Science Foundation of China (Grant Nos.71471075, 11501373, 11701380) and 2015 Scientific Research Project of Shaoguan University (Grant No.S201501017).
WANG Minghui,LIU Xiangdong,LI Yin. A Semiparametric Estimation of a Regression Function in the Partially Linear Autoregressive Model[J]. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2020, 36(1): 26-40.