一种生存数据非线性充分降维子空间估计的新方法

doi:10.3969/j.issn.0253-2778.2015.09.001

中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (9): 709-716.DOI: 10.3969/j.issn.0253-2778.2015.09.001

• 论著 •

一种生存数据非线性充分降维子空间估计的新方法

崔文泉，吴成龙

中国科学技术大学管理学院统计与金融系，安徽合肥 230026

收稿日期:2015-03-03 修回日期:2015-05-21 接受日期:2015-05-21 出版日期:2015-05-21 发布日期:2015-05-21
通讯作者: 崔文泉
作者简介:崔文泉(通讯作者)，男，1964年生，博士. 研究方向：数理统计. E-mail：wqcui@ustc.edu.cn
基金资助:
安徽省自然科学基金（1308085MA02），中国科学院知识创新工程（KJCX3-SYW-S02）资助.

An approach to estimating nonlinear sufficient dimension reduction subspace for censored survival data

CUI Wenquan, WU Chenglong

Department of Statistics and Finance, School of Management, University of Science and of Technology of China,Hefei 230026, China

Received:2015-03-03 Revised:2015-05-21 Accepted:2015-05-21 Online:2015-05-21 Published:2015-05-21

摘要/Abstract

摘要： 给出了一种估计生存数据非线性充分降维子空间的新方法. 利用再生核Hilbert空间性质以及双切片思想，建立广义特征谱分解问题与获得充分降维子空间的联系，以此估计生存时间和删失时间的联合非线性降维中心子空间. 进一步结合SDR中心子空间的性质，通过联合SDR中心子空间来估计权重函数，在算法实现过程中，利用迭代思想，达到提高估计效率的目的.最后通过数值模拟来说明该方法的优良性.

关键词: 再生核Hilbert空间, 充分降维, 切片逆回归, 生存数据

Abstract: An approach was proposed to estimating the nonlinear sufficient dimension reduction (SDR) subspace for survival data with censorship. Based on the theory of reproducing kernel Hilbert spaces (RKHS) and the double slicing procedure，the joint nonlinear sufficient dimension reduction central subspace was estimated by means of the generalized eigen-decomposition equation. And the weight function was estimated by the definition and property of SDR central subspace. The efficiency was improved by the iteration method while the algorithm was being implemented. Finally， the performance of the proposed method was illustrated on simulated data.

Key words: RKHS, sufficient dimension reduction, sliced inverse regression, survival data

中图分类号:

O212

崔文泉，吴成龙. 一种生存数据非线性充分降维子空间估计的新方法[J]. 中国科学技术大学学报, 2015, 45(9): 709-716.

CUI Wenquan, WU Chenglong. An approach to estimating nonlinear sufficient dimension reduction subspace for censored survival data[J]. Journal of University of Science and Technology of China, 2015, 45(9): 709-716.

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一种生存数据非线性充分降维子空间估计的新方法

An approach to estimating nonlinear sufficient dimension reduction subspace for censored survival data

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