Statistical Inference Of Dependent Competing Risks Model

In this paper,the parameter estimation of the dependent competing risks model are mainly considered by using the Marshall-Olkin bivariate Weibull distribution.First,the competing risks model and the Marshall-Olkin bivariate Weibull distribution are briefly described.Then we study three methods to estimate the unknown parameters: the maximum likelihood method,objective Bayesian method and fiducial inference approach.For the maximum likelihood method,we derive the Fisher information matrices of the original parameters and new parameters,then calculate the maximum likelihood estimates of the Marshall-Olkin bivariate Weibull distribution.In terms of the objective Bayesian method,the reference priors based on different grouping orders are explored and the propriety of the posteriors under each prior are checked before doing Bayesian analysis.The specific posterior sampling procedure is also provided to obtain Bayesian estimation.For the fiducial inference,the generalized fiducial distributions of the unknown parameters are obtained,and the corresponding sampling procedure is provided.At last,three methods are applied to analyze a real data set.Based on the fiducial estimates of the example,we conduct some simulation studies.In the simulation,fiducial estimates are compared with maximum likelihood estimators and Bayesian estimates for different sample sizes.The root mean squared error,coverage probability and average length of 95% fiducial(confidence or credible)interval are calculated for comparison.