Maximum Likelihood Estimation For Competing Risk Mixture Model With Grouped Data

In this paper,we study some asymptotic properties of MLE for parameters in the competing risk mixture model with grouped data.Under some proper conditions,we show that MLE is strongly consistent and asymptotically normal.Furthermore,we get the asymptotic distribution of the estimation for the ratio between competing risks.There are four parts in this paper:1.Introduction.In this part,we introduce some basic knowledge for this paper.First,we introduce the definitions of grouped data and MLE,as well as the properties of MLE.Second, we introduce some important theorems we use in this paper.2.Model description and likelihood function with grouped data.In this part,we give the description of the competing risk mixture model and the likelihood function with grouped data.3.Asymptotic properties of MLE.This is the core part of the whole paper.We study the maximum likelihood estimation for the parameters of the competing risk mixture model. Furthermore,we also prove consistency and asymptotic normality of MLE.4.The asymptotic distribution of the estimation for the ratio between competing risks.In this part,based on the results in part three,we get the result by using the method ofδ.