Robust estimation of the generalised partial linear model with missing covariates

Abstract

In this paper, we propose robust estimation of the generalised partial linear model with covariates missing at random. The developed approach integrated the robust method and the method for dealing with missing data. Under some regularity conditions, we establish the asymptotic normality of the proposed estimator of the regression coefficients and show that the proposed estimator of the nonparametric function can achieve the optimal rate of convergence. It can be observed that the regression spline approach avoids some of the intricacies associated with the kernel method, and the robust estimation and inference can be carried out operationally as if a generalised linear model were used. Simulation studies are conducted to investigate the robustness of the proposed method. At the end, the proposed method is applied to a real data analysis for illustration.

Keywords:

• generalised partial linear models
• missing covariates
• regression spline
• robustness
• weighted method

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (10801039, 10931002, 1091120386) the National 985 project of Fudan University and Shanghai Leading Academic Discipline Project, Project number: B118.