Dimension reduction estimation for probability density with data missing at random when covariables are present

doi:10.1016/j.jspi.2016.08.007

CSpace > 应用数学研究所

	Dimension reduction estimation for probability density with data missing at random when covariables are present
	Deng, Jianqiu; Wang, Qihua
	2017-02-01
发表期刊	JOURNAL OF STATISTICAL PLANNING AND INFERENCE
ISSN	0378-3758
卷号	181 页码:11-29
摘要	We develop dimension reduction estimating methods for probability density with data missing at random in the presence of covariables. In this paper, we propose two families of sufficient dimension reduction based nonparametric density estimators by modifying the regression calibration estimator and the inverse probability weighted estimator due to Wang (2008). The proposed methods overcome the challenges faced with high dimensional covariates: model specification and curse of dimensionality. The curse of dimensionality is overcome by replacing the covariables Xi in the regression calibration estimator and the inverse probability weighted estimator, respectively, with a root-n consistent estimator (S) over cap (X-i) of a score S(X-i) for i = 1, 2,..., n. Three different scores S(center dot) are found by dimension reduction techniques. It is shown that the two families of proposed estimators are asymptotically normal, respectively, by taking three different scores. The asymptotic variances are the same when the same score is taken. With different scores, the asymptotic variances are different. A comparison for the two families of density estimators is made by taking different scores. Simulations are carried out to demonstrate the excellent performances of the proposed methods. A real data analysis is used to illustrate our methods. (C) 2016 Elsevier B.V. All rights reserved.
关键词	Kernel density estimation Kernel regression Dimension reduction Missing at random Asymptotic normality
DOI	10.1016/j.jspi.2016.08.007
语种	英语
资助项目	National Natural Science Foundation of China[11171331] ; National Natural Science Foundation of China[11331011] ; National Natural Science Foundation of China[61621003]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000388784800002
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24200
专题	应用数学研究所
通讯作者	Wang, Qihua
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Deng, Jianqiu,Wang, Qihua. Dimension reduction estimation for probability density with data missing at random when covariables are present[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE,2017,181:11-29.
APA	Deng, Jianqiu,&Wang, Qihua.(2017).Dimension reduction estimation for probability density with data missing at random when covariables are present.JOURNAL OF STATISTICAL PLANNING AND INFERENCE,181,11-29.
MLA	Deng, Jianqiu,et al."Dimension reduction estimation for probability density with data missing at random when covariables are present".JOURNAL OF STATISTICAL PLANNING AND INFERENCE 181(2017):11-29.