Application Of Copula In Multivariate Survival Analysis

When using data for decision-making or scientific analysis,it is necessary to consider whether the data may fail to recovery the population due to incompleteness.However,the real data is always incomplete,which may cause the models used for prediction and analysis to fail to be identification or induce inference bias.The purpose of this dissertation is to develop the statistical method dealing with the incompleteness of the multivariate data.In the first part of this thesis,we propose a-step estimator of the semipara-metric copula parameter.When the initial estimator is consistent but lacks the information of the convergence rate,we show it can be upgraded to a rank-based semiparametric efficient estimator.If the initial estimator is rank-based and has con-vergence rate9)^-for 0<?1/2,we show a very small iteration number of Newton algorithm could ensure the approximation has the same efficient asymptotic variance as the one when the iteration number goes to infinite.A Volterra and Fredholm integro-differential equation numerical method is proposed to calculate the proposed-step estimator.We conduct simulations for several general copulas to explain our theoretical results and confirm that the proposed method performs very well.Secondly,we consider the problem of divide and conquer estimation for multivari-ate survival data.We propose a divide and conquer estimation method of Kendall's tau which enables to nonparametrically deal with high dimensional covariates.And apply it into the estimation of some popular copula model.Simulations show that compared to the estimator didn't involve covariate information,our method largely improves bias and variance.The proposed method is applied to Busselton Population Health Surveys to study the dependence between survival times of family members under cardiovascular disease.Next,we consider divide and conquer estimation for hazard function through the marginal modeling approach of multivariate survival data.We separately propose divide and conquer estimation methods for the Euclid parameter,baseline hazard function under shape constrain and baseline hazard function without constraining.Based the estimation of marginal information,we propose a distributed version ofstep estimation of copula parameter.Simulation results imply that our method improves computation time or mean square error.We apply the method on Busselton Population Health Surveys dataset to study the hazard function of family members under cardiovascular disease.Finally,through copula modeling,we propose a semiparametric identification condition for multivariate missing data.The estimation for marginal conditional distribution,density and joint conditional density are provided with also their con-vergence rate.When the observations are categorical variables,we give examples the model fails to be identification,and then construct an identified set and confidence set for the joint distribution of latent variables.The confidence set is also provided.For mix variables observations,we show examples of the model success to be identified.Simulations show that under missing data our method is a consistent estimator,in categorical and mixed cases,the confidence set we construct performs well.