响应变量缺失下部分线性模型均值的稳健估计

郭东林; 薛留根; 胡玉琴

doi:10.11936/bjutxb2016040017

响应变量缺失下部分线性模型均值的稳健估计

doi: 10.11936/bjutxb2016040017

1.
北京工业大学应用数理学院, 北京 100124
2.
商丘师范学院数学与信息科学学院, 河南商丘 476000
3.
浙江财经大学数据科学学院, 杭州 310018

基金项目: 国家自然科学基金资助项目(11571025)

详细信息

作者简介:
作者简介: 郭东林(1982—), 男, 博士生研究生, 讲师, 主要从事复杂数据统计推断方面的研究, E-mail:gdl1105@emails.bjut.edu.cn

中图分类号: O212.7
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出版历程
- 收稿日期: 2016-04-07
- 网络出版日期: 2022-09-13
- 刊出日期: 2017-02-01

Robust Estimation of Mean in Partially Linear Model With Missing Responses

1.
College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
2.
School of Mathematics and Information Science, Shangqiu Normal University, Shangqiu 476000, Henan, China
3.
School of data science, Zhejiang University of Finance and Economics, Hangzhou 310018, China

摘要

摘要: 为了提高估计的稳健性,基于协变量平衡倾向得分和增强的逆概率加权方法,得到了响应变量随机缺失下部分线性模型总体均值的稳健估计,证明了相应估计量具有渐近正态性,利用所得结果构造了总体均值的置信区间.
- 部分线性模型 /
- 随机缺失 /
- 协变量平衡倾向得分 /
- 广义矩估计 /
- 增强的逆概率加权 /
- 稳健估计
Abstract: To improve the robustness of an estimator, based on the covariate balancing propensity score and the augmented inverse probability weighted methods, a robust estimator of the population mean was obtained for the partially linear model, when the responses were missing at random. It is proved that the proposed estimator is asymptotically normal, and hence it can be applied to constructing the confidence region of the population mean.
- partially linear model /
- missing at random /
- covariate balancing propensity score /
- generalized method of moments (GMM) /
- augmented inverse probability weighted /
- robust estimation
The authors have declared that no competing interests exist.

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表 1 基于不同倾向得分方法得到的双稳健估计量的偏差和根均方误差

Table 1. Biases and RMSE of the double robust estimator based on different propensity score estimation methods

情形	n	GLM	CBPS1	CBPS2
2个模型都正确	200	-0.0079(2.8258)	0.0031(2.8108)	0.0092(2.8531)
	500	-0.0014(1.7690)	-0.0022(1.6961)	-0.0047(1.7998)
缺失概率模型正确	200	0.0857(4.0401)	0.0455(3.4427)	0.0633(3.5009)
	500	-0.0111(2.5533)	0.0055(2.2617)	0.0098(2.2600)
回归模型正确	200	-0.0011(3.3738)	-0.0037(2.8609)	-0.0032(2.7145)
	500	0.0126(2.1230)	0.0017(1.8127)	0.0002(1.7810)
2个模型都错误	200	-4.4678(10.0557)	-1.9548(4.2447)	-1.9282(4.1409)
	500	-8.2405(30.7522)	-2.8219(3.8249)	-2.8523(3.7897)
注:括号内的值表示双稳健估计量的根均方误差.

下载: 导出CSV

表 2 μ的95%置信区间的平均区间长度和相应覆盖概率

Table 2. Average lengths and coverage probabilities of the 95% confidence intervals for μ

情形	n	GLM	CBPS1	TRUE
2个模型都正确	200	0.6691(0.944)	0.6385(0.945)	0.6609(0.948)
	500	0.4289(0.946)	0.4126(0.946)	0.4295(0.949)
缺失概率模型正确	200	0.7531(0.932)	0.6958(0.935)	0.7254(0.938)
	500	0.4962(0.945)	0.4652(0.950)	0.4849(0.946)
回归模型正确	200	0.8742(0.945)	0.6670(0.946)	0.6644(0.947)
	500	0.6769 (0.948)	0.4317 (0.949)	0.4253(0.951)
2个模型都错误	200	0.8999(0.887)	0.7475(0.888)	0.7464(0.940)
	500	0.9258(0.843)	0.5130(0.846)	0.4853(0.945)
注:括号内的值表示覆盖概率,TRUE表示利用真实概率的情形.

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