Depth-based weighted empirical likelihood and general estimating equations

Abstract

In this paper, we link the depth-based weighted empirical likelihood (WEL) with general estimating equations to produce a robust estimation of parameters for contaminated data with auxiliary information about the parameters. Such auxiliary information can be expressed through a group of functionally independent general estimating equations. Under general conditions, asymptotic properties of the WEL estimator are established. Furthermore, we prove that the WEL ratio statistic is asymptotically chi-squared distributed. Simulation studies are conducted to test the robustness of the WEL estimator. Finally, we apply the proposed method to analyse the gilgai survey data.

Keywords:

• weighted empirical likelihood
• general estimating equations
• depth function
• robustness

AMS Subject Classifications :

• 62G05
• 62G20
• 62G35
• 62H12

Acknowledgements

Xueqin Wang was partially supported by NSFC under Grant No. 11001280, Doctoral Fund of Ministry of Education of China under Grant No. 20090171110017, Natural Science Foundation of Guangdong Province under Grant No. 10151027501000066 and SRF for ROCS, SEM. Shaoli Wang's work was sponsored by Shanghai Pujiang Program, and was also partially supported by Shanghai University of Finance and Economics through Project 211 Phase III and Shanghai Leading Academic Discipline Project, Project Number: B803.