Statistical Inference On Dependent Right-censored Data

In the study of sociology,medicine,industrial technology and economics,because the failure time may be longer than the upper limit of the observation time,to reduce the cost,people always take the censoring method to deal with this problem.But this method lead to the existence of the censored data.In the study of the failure time data,how to deal with the censored data is the major topic.In the study of right-censored data(7)T,?(8),many papers was based on the assumption that the failure time and the censored time is independent.But in fact,the assumption is not always correct.The study about dependent censored data is very necessary.so a assumption between the censored time and the failure time is very important.Now we make these hypothesis:The relationship between the censored time and the failure time is described by copula functions;The joint distribution of the censored time and the failure time is described by copula functions about their marginal distributions.By studying the joint distribution of the censored time and the failure time,we study the statistical problem about dependent censoring in different models.In this paper,we focus on the right-censored data and study the exponential distribution of parametric models and cox proportional hazard model.We take profile likelihood method to construct the likelihood functions in different models.We use the iterative calculation to solve likelihood functions.To describe the efficiency of method,we make sensitivity analysis by changing the copula functions and its parameters.The result shows that the result of statistical inference about copula functions is stable,but the result also shows that the result of statistical inference about its parameter is sensitive.