缺失数据下的线性泛函的半参数降维推断

J4 ›› 2011, Vol. 46 ›› Issue (4): 17-22.

缺失数据下的线性泛函的半参数降维推断

祝丽萍^1,2,邵伟¹

1.山东大学数学学院, 山东济南 250100; 2.昌吉学院数学系, 新疆昌吉 831100

收稿日期:2010-12-01 发布日期:2011-04-21
作者简介:祝丽萍(1973- ),女,讲师,博士研究生,研究方向为非参数统计. Email:lipingzhu2002@163.com
基金资助:
新疆维吾尔自治区高校青年教师科研启动基金资助项目(XJEDU2008563)

Linear functionals semiparametric dimension reduction inference with missing data

ZHU Li-ping^1,2, SHAO Wei¹

1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China;
2. Department of Mathematics, Changji College, Changji 831100, Xinjiang, China

Received:2010-12-01 Published:2011-04-21

摘要/Abstract

摘要：

针对缺失数据下线性泛函估计中存在的非参数高维问题和模型参数化后的稳健性问题,本文提出了线性泛函估计的半参数降维推断方法, 通过非参数函数估计来插补线性泛函,并用参数工作函数来降维。所得半参数降维估计具有双稳健的特点,即只要选择概率函数正确参数化或者降维插补指标可以修复线性函数的条件期望,所得估计就是相合的，而且两者都满足时,估计达到最优。

关键词: 线性泛函;缺失数据;降维

Abstract:

A semiparametric dimension reduction method is proposed to reconcile the nonparametric regression approach and the model-based approaches in estimating linear functionals with missing data. The linear functionals are estimated through nonparametric functionals estimation, where the dimension is reduced by a parametric working index. The proposed estimator is robust to model misspecification: it is always consistent either the selected probability is correctly specified or the working index can recover the conditional linear functionals given the covariates. In addition, when both above conditions are satisfied, the proposed estimator attains the optimal efficiency.

Key words: linear functionals; missing data; dimension reduction

祝丽萍1,2,邵伟1. 缺失数据下的线性泛函的半参数降维推断[J]. J4, 2011, 46(4): 17-22.

ZHU Li-ping1,2, SHAO Wei1. Linear functionals semiparametric dimension reduction inference with missing data[J]. J4, 2011, 46(4): 17-22.

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