Statistical Inference Of Competitive Risk Models Under Complex Censored Data

This paper focuses on the statistical inference of independent and dependent competitive risk models under different complex censored data,including parameter point estimation,interval estimation,Bayesian estimation,goodness-of-fit tests,power analysis,censoring scheme optimization and data simulations.The paper consists of three parts: the first part is the statistical inference of the independent competitive risk model under progressive type Ⅱ censored data with binomial removals.The study is conducted under the assumptions of a constant multistage accelerated lifetime experimental model.The experimental individuals are supposed to follow the Pareto distribution.We sequentially discuss the existence and uniqueness of maximum likelihood estimates of parameters.Bayesian estimates based on symmetric and asymmetric loss functions and the highest posterior density confidence interval are proposed.Then,the goodness-of-fit test and power analysis are performed based on the two proposed statistics.Next,based on adaptive type Ⅱ progressive hybrid censored data,statistical inferences are discussed for mutually independent competitive risk models,and experimental individual lifetimes follow a two-parameter Burr-XⅡ distribution.Based on the maximum likelihood estimates,the approximate confidence intervals are established based on the pivot quantities,and the Bootstrap method is used to derive confidence intervals for the small sample case.The derivation and data simulation related to the optimization of the censoring scheme are carried out according to the three optimization criteria.Finally,the statistical inference of the adaptive type Ⅱ progressive hybrid censored data is carried out for the dependent competitive risk model.And the Marshall-Olkin bivariate exponential distribution is chosen as the experimental individual lifetime distribution according to the characteristics of dependent risk.Approximate confidence intervals based on the Delta method are derived in maximum likelihood estimation.The flexible Gamma-Dirichlet distribution is chosen as the prior distribution for Bayesian estimation using the Metropolis-Hastings algorithm.Monte Carlo simulations are also performed to compare the performance of various estimation methods.The algorithm to generate censored samples under different distributions is proposed in the paper.In the data simulations,the performance is judged based on the mean square error,interval coverage and average interval width.Three actual data sets have been analyzed to verify the effectiveness and feasibility of the proposed various methods.There are 7 figures,37 tables and 50 references in this thesis.