排序集抽样下随机删失数据的非参数估计

项目名称： 排序集抽样下随机删失数据的非参数估计

项目编号： No.11426083

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 董晓芳

作者单位： 河北经贸大学

项目金额： 3万元

中文摘要： 排序集抽样方法适用于样本测量困难但排序容易的场合，该抽样下完全数据的非参数统计已有大量的研究成果。然而，在生存分析中经常碰到的是随机删失数据。因而，排序集抽样下随机删失数据的非参数统计研究具有重要的理论和实践意义。 本项目研究排序集抽样下随机删失数据的非参数估计问题。研究内容分为两部分，一是总体生存函数的乘积限估计，包括强相合性的证明、估计效率的比较；二是总体概率密度函数的核密度估计，包括估计量的建立、强相合性和渐近正态性的证明、估计效率的比较。本项目利用排序集样本性质和概率统计知识，借助已有的研究结果，采用理论分析与数值模拟相结合的手段，对研究内容进行分析和推断。 本项目的研究结果不仅为其它生存指标如风险率函数、平均寿命等估计问题提供了思路，也为其它统计问题如假设检验、回归分析等奠定了坚实的基础。另外，研究结果在临床医学、生态环境等领域都有广泛的应用前景。

中文关键词： 排序集抽样；随机刪失数据；非参数估计；生存函数；概率密度函数

英文摘要： Ranked set sampling protocol is appropriate for situations in which quantification of sampling units is difficult but ranking of the units is easy. There are large numbers of research achievements about nonparametric statistics of complete data under ranked set sampling. However, random censored data is often found in survival analysis. Therefore, it has important theoretical and practical significance to study nonparametric statistics of random censored data under ranked set sampling. The project studies the nonparametric estimation of random censored data under ranked set sampling. The content of this project is divided into two parts. The first part is the product-limit estimation of the population survival function, which includes the proof of strong consistency and the comparison between estimation efficiencies. The second part is the kernel density estimation of the population probability density function, which includes the construction of estimator, the proof of strong consistency and asymptotic normality, and the comparison between estimation efficiencies. To analyze and infer the research content, the project need to use the properties of ranked set sample and the knowledge of probability and statistics, draw support from the previous research results, and adopt the means that combining theor

英文关键词： ranked set sampling；random censored data；nonparametric estimation；survival function；probability density function