Re-Weighted Least Squares Estimation with Censored and Grouped Data: An Application of the EM Algorithm

SUMMARY We consider the problem of adapting weighted least squares estimation so that estimates can be found with censored or grouped data. The EM algorithm is implemented for the linear model where the errors are assumed to be generated by a scale mixture of normal distributions. In particular, explicit results are given for the case where the marginal distribution of the error is Student-t with an even number of degrees of freedom. Expressions for the observed information are found, relating grouped data results to those for right censored data. Some ad hoc rules for the identification of outliers are given. An example involving the lifetimes of motorettes is considered.