相依右删失数据的统计推断
发布时间：2019-01-12 11:28
【摘要】：在诸如社会学、医疗、工业技术、经济学和流行病学等领域的时间数据的研究中,考虑到,部分研究对象其实际的失效时间可能超出观测时间的上限,为成本计,人们通常会采用删失的方法进行处理。这会造成删失数据的存在。如何处理和分析删失数据是失效时间数据分析中的主要内容。关于右删失数据(T,?)的研究,大多数都是基于独立删失(Independent censoring or Non-informative censoring)假定进行的,即失效时间和删失时间相互独立。但是在很多实际问题中,这种独立假设常常不成立。因此相依删失的研究十分必要。在相依删失数据下,必须对删失时间和失效时间的相依关系进行描述。假定删失时间和失效时间的相依关系可以由一个copula函数表示。失效时间和删失时间的联合分布可以表示为它们边际分布的copula函数,通过对这个联合分布函数进行讨论,可以对于不同模型进行统计推断。本文主要对相依右删失数据进行了讨论。本文主要基于两种模型进行研究:指数分布模型、cox比例风险模型。基于失效时间变量和删失时间变量的copula模型采用截面似然(profile likelihood)的办法构造似然函数,利用迭代计算的方法对似然函数进行求解。同时为了说明方法的有效性,本文还对copula函数和copula函数中的参数进行敏感性分析。模拟计算结果显示,统计推断的结果关于copula函数比较稳健,但是对于copula函数中的参数十分敏感。
[Abstract]:In the study of time data in areas such as sociology, medicine, industrial technology, economics and epidemiology, it was considered that some of the subjects' actual failure times might exceed the upper limit of the observed time and be costing. People usually use censored methods to deal with it. This results in the existence of censored data. How to deal with and analyze censored data is the main content of failure time data analysis. On right censored data Most of the researches in this paper are based on the assumption of independent censored (Independent censoring or Non-informative censoring, that is, the time of failure and the time of deletion are independent of each other. But in many practical problems, this independent assumption is often not true. Therefore, the study of dependent deletion is very necessary. Under the dependent censored data, we must describe the dependent relationship between the deletion time and the failure time. It is assumed that the dependence of the deletion time and the failure time can be represented by a copula function. The joint distribution of failure time and censored time can be expressed as the copula function of their marginal distribution. In this paper, we mainly discuss the right censored data. This paper is mainly based on two models: exponential distribution model and cox proportional risk model. The copula model based on the failure time variable and the censored time variable uses the cross-section likelihood (profile likelihood) method to construct the likelihood function, and the iterative calculation method is used to solve the likelihood function. In order to illustrate the validity of the method, the sensitivity of the parameters in copula function and copula function is also analyzed. The simulation results show that the result of statistical inference is robust for copula function, but sensitive to the parameters in copula function.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
本文编号：2407721
[Abstract]:In the study of time data in areas such as sociology, medicine, industrial technology, economics and epidemiology, it was considered that some of the subjects' actual failure times might exceed the upper limit of the observed time and be costing. People usually use censored methods to deal with it. This results in the existence of censored data. How to deal with and analyze censored data is the main content of failure time data analysis. On right censored data Most of the researches in this paper are based on the assumption of independent censored (Independent censoring or Non-informative censoring, that is, the time of failure and the time of deletion are independent of each other. But in many practical problems, this independent assumption is often not true. Therefore, the study of dependent deletion is very necessary. Under the dependent censored data, we must describe the dependent relationship between the deletion time and the failure time. It is assumed that the dependence of the deletion time and the failure time can be represented by a copula function. The joint distribution of failure time and censored time can be expressed as the copula function of their marginal distribution. In this paper, we mainly discuss the right censored data. This paper is mainly based on two models: exponential distribution model and cox proportional risk model. The copula model based on the failure time variable and the censored time variable uses the cross-section likelihood (profile likelihood) method to construct the likelihood function, and the iterative calculation method is used to solve the likelihood function. In order to illustrate the validity of the method, the sensitivity of the parameters in copula function and copula function is also analyzed. The simulation results show that the result of statistical inference is robust for copula function, but sensitive to the parameters in copula function.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
【参考文献】
相关期刊论文 前1条
1 徐安察;汤银才;;基于Copulas加速寿命试验中竞争失效模型的统计分析(英文)[J];应用概率统计;2012年01期
，本文编号：2407721
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