Title（问题）：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）下昼2:00-3:00

Place（所在）：北京大学理科一号楼1303课堂

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（报告人先容）：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，国家优异青年基金获得者
。

王启华教授出书专著三部，Springer出书社出书的书两章, 揭晓论文80余篇， 其中54篇揭晓在JASA，The Annals of Statistics与Biometrika等国际主要刊物，一些论文被普遍引用，特殊是他与相助者所生长的调解履历似然要领被许多顶尖级刊物文章所使用，对履历似然要领的生长起到了推行动用
。

曾获得天下第五届钟家庆数学奖、首界天下优异博士论文等奖
。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》等国际海内刊物编委
。