【作者】 李敏；

【导师】 丁帮俊；

【作者基本信息】 华东师范大学 ， 统计学， 2021， 硕士

【摘要】 与失效时间相关的数据经常会由于客观原因的限制无法得到准确值,样本往往会是一组区间数据.其删失类型又分为独立删失与相依性删失,顾名思义,独立删失指的就是失效时间与删失时间相互独立,两者不存在任何的相关关系,否则就属于相依性删失的范畴.关于区间数据,现在已经有大量的研究成果,但是大部分都是在独立删失的假设下得到的,若对相依性区间数据采用这些统计方法,那就会忽略很多关于相依性的信息,得到的估计可能偏差较大,甚至严重偏离真实情况.故本文运用将相依性纳入考虑的Copula模型方法对相依Ⅱ型区间数据进行相应的统计分析,首先利用Copula函数的‘连接’本质构造出似然函数,然后利用Nelder-Mead算法极大化似然函数求得参数的估计值.另外,不同于从生存函数角度出发,本文利用Copula函数表示的联合分布函数推导出了区间数据的似然函数,不仅给出了独立删失下两类区间数据和相依I型区间数据似然函数的新推导过程,还给出了相依Ⅱ型区间数据的推导过程和表达式.最后数值模拟的结果也显示运用本文提出的似然函数进行极大似然估计得到的估计结果比较接近于真实值且比较稳健,这对将本文提出的似然函数应用到区间数据的极大似然估计法中提供了一定的理论支持.更多还原

【Abstract】 Due to the limitation of objective reasons,the data related to the failure time often can not get the accurate value,and the sample is often a group of interval censored data.The types of censoring are divided into independent censoring and dependent censoring.As the name suggests,independent censoring means there is no correlation between them.There are a lot of research results about interval censored data,but most of them are obtained under the assumption of independent censoring.If we use the statistical method of independent censoring for dependent interval censored data,we will ignore a lot of information about dependence.In this paper,we will use copula model to analyze the dependent type II interval censored data.First,we use copula function to construct the likelihood function,and then use Nelder Mead algorithm to maximize the likelihood function to get the estimation of parameters.In addition,unlike from the perspective of survival function,this paper constructs the likelihood function of interval censored data from the joint distribution function constructed by copula function.It not only gives the new derivation process of the likelihood function of two types of independent interval censored data and dependent type I interval censored data,but also gives the derivation process and expression of dependent type II interval censored data.Finally,by the simulation,we can know that the MLE obtained by using the proposed likelihood function are more accurate and more robust,which provides some theoretical support for applying the proposed likelihood function to the maximum likelihood estimation method on interval censored data.更多还原