长度偏差右删失数据剩余寿命的分位数回归

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长度偏差右删失数据剩余寿命的分位数回归孙桂萍^1,2, 厉诚博³, 周勇^4,51 上海财经大学统计与管理学院上海 200433;
2 枣庄学院数学与统计学院枣庄 277100;
3 东北财经大学统计学院大连 116025;
4 华东师范大学经管学部统计交叉科学研究院上海 200062;
5 中国科学院数学与系统科学研究院北京 100190 Quantile Residual Regression with Length-Biased and Right-Censored Data Gui Ping SUN^1,2, Cheng Bo LI³, Yong ZHOU^4,51 School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China;
2 School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277100, P. R. China;
3 School of Statistics, Northeast University of Finance and Economics, Dalian 116025, P. R. China;
4 Faculty of Economics and Management, East China Normal University, Shanghai 200062, P. R. China;
5 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

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摘要本文研究长度偏差数据下剩余寿命分位数模型的估计方法，充分考虑有偏抽样机制对模型估计的影响.如果忽略这种有偏性会导致估计产生严重偏差甚至错误的结果.本文首先针对长度偏差右删失数据的剩余寿命分位数提出了对数形式的线性回归模型，对删失变量与协变量独立和不独立的两种情况利用估计方程给出了模型参数的估计.其次，通过经验过程和弱收敛理论给出了参数估计的相合性和渐近正态性.最后，本文对提出的估计方法进行了数值模拟并用该方法对奥斯卡奖数据进行分析.

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收稿日期: 2018-10-17

MR (2010):	O212
	O212.1

基金资助:国家自然科学重大研究计划重点项目（91546202）；国家自然科学基金委重点项目（71931004）

作者简介: 孙桂萍,E-mail:sunguiping1008@163.com;厉诚博,E-mail:lichengbo@dufe.edu.cn;周勇,E-mail:yzhou@amss.ac.cn

引用本文:

孙桂萍, 厉诚博, 周勇. 长度偏差右删失数据剩余寿命的分位数回归[J]. 数学学报, 2020, 63(1): 1-18. Gui Ping SUN, Cheng Bo LI, Yong ZHOU. Quantile Residual Regression with Length-Biased and Right-Censored Data. Acta Mathematica Sinica, Chinese Series, 2020, 63(1): 1-18.

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[1]	刘玉涛, 潘婧, 周勇. 右删失长度偏差数据分位数差的非参数估计[J]. 数学学报, 2020, 63(2): 105-122.
[2]	厉诚博, 胡淑兰, 周勇. 长度偏差右删失数据下[1mm]比例均值剩余寿命模型的估计方法[J]. 数学学报, 2018, 61(5): 865-880.

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