排序集抽样下截尾数据估计问题的研究

Ranked set sampling method is appropriate for situation in which visual ranking of sampling units is easy but quantification of the units is difficult. There have been large numbers of research achievements about statistical inference of complete data under ranked set sampling. Considering that truncated data is often found in life test, the project studies estimation problems of two kinds of truncated data with fixed time and with fixed number under ranked set sampling. . The content of this project is divided into three parts. The first part studies nonparametric estimation problems of survival function, hazard rate function and life expectancy by adopting the average rank product-limit estimation, the kernel estimation and the mean type functional estimation respectively, which includes construction of estimators, analysis of statistical properties, and comparison between estimation efficiencies. The second part studies maximum likelihood estimation problems of parameters of exponential distribution, Weibull distribution and lognormal distribution by adopting the partial expectation method and the iterative method. The third part presents new ranked set sampling methods, and gives the optimal sampling method of each estimation problem by combining the first two parts of research content.. To analyze the research content, the project adopts the means that combining theoretical analysis, numerical simulation and practical application. The research results of this project lay the solid theoretical foundation for problems of truncated data such as hypothesis testing, regression analysis and so on. In addition, the research results have extensive application prospect in clinical medicine, environment sciences, reliability engineering and so on.

排序集抽样方法适用样本易于直观排序但不易于具体测量的场合，该抽样下完全数据的统计推断已有大量研究成果。考虑到寿命试验经常得到的是截尾数据，本项目研究排序集抽样下定时和定数两种截尾数据的估计问题。. 本项目研究内容分为三部分：一是采用均秩型乘积限估计、核估计和均值型泛函估计方法，分别研究生存函数、风险率函数和平均寿命的非参数估计问题，包括估计量的构建、统计性质的分析和估计效率的比较；二是采用部分期望法和迭代法，研究指数分布、Weibull分布和对数正态分布参数的极大似然估计问题；三是提出新的排序集抽样方案，结合前两个研究内容，给出各个估计问题的最优抽样方案。. 本项目采用理论推导、数值模拟和实际应用相结合的手段对研究内容进行分析。研究结果不仅为截尾数据的假设检验、回归分析等问题奠定了坚实的理论基础，也在临床医学、环境科学、可靠性工程等领域有着广泛的应用前景。

排序集抽样方法适用样本易于直观排序但不易于具体测量的场合，此抽样方法已被广泛应用到临床医学、环境科学、可靠性工程等领域。考虑到寿命试验经常得到的是截尾数据，本项目研究了排序集抽样下截尾数据的估计问题。.本项目的主要研究内容和重要结果为：一是采用均秩型乘积限估计、核估计和均秩型泛函估计方法，分别构建了可靠性函数、风险率函数和平均寿命的非参数估计量，分析了这些新估计量的统计性质，比较了这些新估计量与简单随机抽样下相应估计量的估计效率，结果表明：排序集抽样方法的抽样效率一致高于简单随机抽样方法；二是给出了指数分布、Weibull分布和对数正态分布参数的似然方程，给出了这些极大似然估计量的迭代算法和修正算法，分析了这些新估计量的统计性质，估计效率的比较结果表明：这些新极大似然估计量及其修正估计量都优于简单随机抽样下相应极大似然估计量；三是研究了广义排序集抽样下寿命指标的非参数估计和寿命分布的参数估计，并根据估计效率给出了最优排序集抽样方案。.本项目的研究结果不仅提高了截尾数据的估计效率，扩大了排序集抽样方法的适用范围，也为截尾数据的假设检验、回归分析等问题奠定了坚实的理论基础。