The EM Algorithm Of MLE Of The Parameters In Censored Linear Regression Models With Unequal Variances

In industry experiments,because of restrain of experiment condition, experiment response is often censored data.In censored linear regression models,standard regression methods is not applicable.It is a ordinary method that treating the censored data as the failure data,then it is analyzed by standard regression methods.But it may result in wrong detemine,because there may be a great difference between censored time and true failure time. So it is necessary finding a method to analyze data. Maximum likelihood estimate is adopted because of its good properties.Maximum likelihood estimate of the parameters in linear models with right censored data is introduced by Aitkin(1981) using the EM algorithm. And prove that EM algorithm and iterative least squares methods are essentially the same except for the estimate of the error variance,δ~2.Iterative convergence is obtained by EM algorithm properties. But there is a problem using maximum likelihood estimateit in censored data models,that is MLE may not existence. For censore linear regression models with same variances,a sufficient and necessary condition is obtained for the existence of MLE by Sivapulle and Burridge(1986) ,Hamada and Tse(1988).And these conditions may be transform to linear programming problem. It is few to existence of MLE and calculation of estimate of the parameters in censored linear regression models with unequal variances in references.In this paper,we consider the existence of MLE in censored linear regression models with unequal variances,a sufficient and necessary condition is obtained for existence of MLE in normal ,and it may be transform to linear programming problem too.Then we propose two steps procedure of obtaining parameter'β, δ_i~2) estimates(β, δ_i~2) by likelihood equation,obtain MLE of parameter by EM algorithm,and we prove thecon-sistency of EM algorithm and this ordinary iterative algorithm, thus ensure its convergence from EM algorithm properties. At the same time.we prove that MLE of regression cofficients are identical to generalized least squares estimate, but those for the variance estimates are different.The biases of the variance estimates are discussed.At last,we describe that estimate accuracy is related to censored time of censored data.