Parameter Estimation Of Finite Mixed Models With Censored Data

As an important branch of modern statistics,the field of survival analysis and reliability has been widely used in many fields of science.In the era of rapid development of information technology,data in various fields are becoming more and more complex,and they may come from different types or grouping,therefore,the mixture models is more and more widely developed and applied in the field of survival analysis and reliability.However the survival analysis and reliability are often accompanied by censored data.Therefore,the mixture models have been studied in this field and have important application value.This paper mainly studies the parameter estimation problem of finite-mixed model under censored data from two aspects.On the one hand,it discusses the accuracy of parameter estimation from the aspect of censored data processing,that is,adopts two processing methods for censored data.The first is only to regard the belonging component of the data as missing information,and the second is to regard the belonging component of the data and the censored data as missing information,and then compare the performance of the two processing methods through simulation;on the other hand,the improvement from the algorithm.In this paper,the stability and accuracy of parameter estimation are discussed.The DAEM algorithm(deterministic annealing)is used to overcome the defect that the EM algorithm converges to the local maximum,thus improving the accuracy of the estimation.For the processing aspect of censored data,the first type only considers the component of the data as missing information,then the probability density function of the default censored data is known,and the probability function is replaced by the survival function;The censored data is also regarded as missing information,and the logarithmic likelihood function of the observed data is expected to obtain the density function.The simulation results show that although the total amount of censored data is different,the two methods based on EM algorithm have almost the same parameter estimation results for the mixed exponential distribution,but in terms of the accuracy of simulations,the results of second method are better than those of the first method.As far as the improvement of the algorithm is concerned,the EM algorithm is difficult to distinguish when the component mean interval is small,and the DAEM algorithm has higher accuracy and the estimation result is more accurate.As the interval of the component mean increases,the estimation results of the two algorithms are obtained.It tends to be consistent,but the DAEM algorithm tends to be more stable.