Title（题目）：Semiparametric efficient estimation and optimal estimation for partially linear single-index models with responses missing at random

Speaker（报告人）：王启华 研究员 (中国科学院数学和系统科学研究院)

Time（时间）：2010年11月18日（周四）下午2:00-3:00

Abstract（摘要）：

In this talk, we establish the semiparametric efficient bound for the heteroscedastic partially linear single-index models with responses missing at random, and develop the augmented inverse probability weighted efficient estimating equation method. By solving the estimating equation, we obtain estimators for the parameter vectors in the linear part and the single index part simultaneously. The estimators are asymptotically semiparametric efficient when both the propensity score function and the conditional probability density function of the response given the covariables (working model) are specified correctly, and are double robust in the sense that both the estimators are consistent if one of the two posited models is specified correctly. The estimating equation concerns the MLE of parameters of both the posited models. Hence, if one of the two posited models are specified errorly, the proposed estimators are inefficient. In the case where the working model is specified errorly and the propensity score model is specified correctly, we improve the efficiency of the estimators by improving the estimating equation. This estimating equation can be improved with the MLE of the parameter of the wrong working model in the estimating equation replaced by a consistent estimator of the minimizer of the asymptotic variances of the estimators on the parameter of the working model. A simulation was conducted to evaluate the proposed methods.

About the speaker（报告人介绍）：王启华教授在北京大学获得博士学位，现为中国科学院数学与系统科学研究院研究员，教育部讲座教授，国家杰出青年基金获得者。

王启华教授出版专著三部，Springer出版社出版的书两章, 发表论文80余篇， 其中54篇发表在JASA，The Annals of Statistics与Biometrika等国际重要刊物，一些论文被广泛引用，特别是他与合作者所发展的调整经验似然方法被很多顶尖级刊物文章所使用，对经验似然方法的发展起到了推动作用。

曾获得全国第五届钟家庆数学奖、首界全国优秀博士论文等奖。是《中国科学》，《现代数学基础丛书》，《应用数学学报》英文版， 《Ann. Inst. Math. Statist.》， 《Journal of Applied Probability and Statistics》等国际国内刊物编委。