正相协及缺失数据情形的经验似然推断

项目名称： 正相协及缺失数据情形的经验似然推断

项目编号： No.11201088

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李英华

作者单位： 广西师范大学

项目金额： 23万元

中文摘要： 正相协(PA)样本在可靠性理论、渗透理论和某些多元分析问题中较为广泛出现，此外在市场调查、临床试验、医药追踪试验等，由于各种人为或其它不可知因素，都容易导致大量的缺失数据的产生。Owen 提出的经验似然方法是近年来新提出的最重要的非参数统计方法之一, 由此方法得到的估计具有良好的统计性质，用经验似然方法研究PA和缺失数据情形的统计推断是统计界非常关注的热门课题，具有重要的理论价值和实际意义。 本项目拟用经验似然方法讨论PA样本下总体分布、总体的一些重要指标和其它常见统计模型的推断，主要研究如下三个专题：(1)在PA样本下对总体的分布和重要指标（如概率密度函数、分位数等）进行经验似然推断；(2)在PA样本下对一些常见统计模型（如线性模型、非参数回归模型）进行经验似然推断；(3)在缺失数据情形对(1)和(2)进行深入研究。希望通过这些研究为实际数据处理工作者提供较优且切实可行的统计应用工具

中文关键词： 相协样本；缺失数据；经验似然；渐近分布；

英文摘要： Positive association occurs often in reliability theory problems, in percolation theory and in certain multivariate analysis problems. In practice,on the other hand, some data may be missing for various reasons such as unwillingness of some sampled units to supply the desired information, loss of information caused by uncontrollable factors,failure on the part of the investigator to gather correct and so forth. The empirical likelihood (EL) method is introduced by Owen and has many other advantages over normal approximation-based methods and the bootstrap method for constructing confidence intervals.We will use the EL method to make inference for the distribution and some important indices of a population and for some important statistical models under positive samples. We notice that there is few literature on the inference under positively associated samples. Our project is an attractive subject in statistical field and has important theoretical value and practical significance. The project firstly will make inference for the distribution and some important indices of the population, for example, probability density function and quantiles, and then make inference for some important statistical regression models under positively associated samples. Finally we will continue to develop above methods under positiv

英文关键词： associated sample；missing data；empirical likelihood；asymptotically distributed；