Dimension reduction estimation for probability density with data missing at random when covariables are present
文献类型：期刊论文
| 作者 | Deng, Jianqiu; Wang, Qihua
|
| 刊名 | JOURNAL OF STATISTICAL PLANNING AND INFERENCE
 |
| 出版日期 | 2017-02-01 |
| 卷号 | 181页码:11-29 |
| 关键词 | Kernel density estimation Kernel regression Dimension reduction Missing at random Asymptotic normality |
| ISSN号 | 0378-3758 |
| DOI | 10.1016/j.jspi.2016.08.007 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000388784800002 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/24199]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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