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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (6): 1001-1010.doi: 10.3969/j.issn.1005-3085.2023.06.011

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长度偏差完全数据下均值剩余寿命的矩类估计

武洪萍   

  1. 山东石油化工学院大数据与基础科学学院，东营 257061
  • 收稿日期:2021-04-13 接受日期:2022-04-29 出版日期:2023-12-15 发布日期:2024-02-15
  • 基金资助:
    国家社会科学基金 (20TJ060)；东营市科学发展基金 (DJ2021023).

Moment-type Estimations of Mean Residual Life Function with Complete Length-biased Data

WU Hongping   

  1. School of Big Data and Fundamental Sciences, Shandong Institute of Petroleum and Chemical Technology, Dongying 257061
  • Received:2021-04-13 Accepted:2022-04-29 Online:2023-12-15 Published:2024-02-15
  • Supported by:
    The National Social Science Foundation of China (20TJ060); the Science Development Fund of Dongying (DJ2021023).

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摘要：

长度偏差数据在寿命研究中是广泛存在的，但是在长度偏差完全样本下对均值剩余寿命的研究却相对较少。作为生存分析中评估个体生存情况的重要指标之一，均值剩余寿命也越来越受到统计研究者的关注。为了在长度偏差完全数据下建立均值剩余寿命函数的非参数估计，采用逆概率加权方法，以矩估计为基础，得到了均值剩余寿命的两种估计量，并证明了两个估计量在适当条件下分别依分布收敛到均值为零的正态变量。为了评估两种点估计在有限样本下的优劣，还进行了一系列的数值模拟试验，并将模拟结果与已有方法进行了比较。数值结果表明了两种估计方法的合理性。

关键词: 剩余寿命, 均值, 长度偏差数据, 矩类估计, 中心极限定理

Abstract:

Length-biased data widely exist in life research. However, there are relatively few studies on the mean residual life under complete length-biased data. As one of the important indicators to evaluate individuals’survival, mean residual life attracts more and more attention from statistical researchers. In order to construct nonparametric estimations of the mean residual life function under complete length-biased data, two estimations are derived by utilizing the idea of moment estimation. It is proved that the proposed estimations converge in distribution to two zero-mean normal variables under moderate conditions, respectively. In order to evaluate the performance of the proposed estimators in finite samples, a series of numerical simulations are carried out, and the simulation results are compared with those of existing methods. The numerical results show the rationality of two proposed estimations.

Key words: residual life, mean, length-biased data, moment-type estimation, central limit theorem

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