Semiparametric efficient inferences for generalised partially linear models

Abstract

In this paper, we consider semiparametric efficient inferences in the generalised partially linear models. A novel bias-corrected estimating procedure and a bias-corrected empirical log-likelihood ratio are developed, respectively, for point estimation and confidence regions for parameters of interest. Under mild conditions, the resulting likelihood ratio is shown to be standard chi-squared distributed asymptotically. Moreover, it is noteworthy that the range of bandwidth in this paper covers the optimal bandwidth due to the implementation of a new bias-corrected technique. Therefore, no undersmoothing is needed here for guaranteeing the asymptotically standard chi-squared distribution of the proposed statistic. Simulation study and real application are also provided in order to illustrate the performance of resulting procedure.

Keywords:

• Generalised partially linear models
• efficient inferences
• weighted estimating equations
• empirical log-likelihood

Acknowledgments

Shihua Luo's research is supported by NSF of China (Grant No. 61973145) and NSF of Jiangxi Province (No. GJJ180247). Yawen Fan's research is supported by the Postgraduate Innovation Project of Jiangxi Province (No. YC2019-S216). Xiaohui Liu's research is supported by NSF of China (Grant Nos. 11971208, 11601197), China Postdoctoral Science Foundation funded project (2016M600511, 2017T100475), the Postdoctoral Research Project of Jiangxi (No. 2017KY10, xskt19393), NSF of Jiangxi Province (Nos. 2018ACB21002, 20171ACB21030). Our thanks also go to two reviewers, the associated editor and the Editor in chief, whose comments have led to many improvements in this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Shihua Luo's research is supported by NSF of China (Grant No. 61973145) and NSF of Jiangxi Province (No. GJJ180247). Yawen Fan's research is supported by the Postgraduate Innovation Project of Jiangxi Province (No. YC2019-S216). Xiaohui Liu's research is supported by NSF of China (Grant No. 11971208, 11601197), China Postdoctoral Science Foundation funded project (2016M600511, 2017T100475), the Postdoctoral Research Project of Jiangxi (No. 2017KY10, xskt19393), NSF of Jiangxi Province (No. 2018ACB21002, 20171ACB21030). Our thanks also go to two reviewers, the associated editor and the Editor in chief, whose comments have led to many improvements in this paper.