Modified maximum likelihood predictors of future order statistics from normal samples

Suppose we have a Type II censored sample consisting of the first r-order statistics of a random sample of size n from a normal population with unknown mean. In this paper, we look at some modified maximum likelihood predictors of the sth-order statistic based on this data, where r < s less than or equal to n. We suggest four types of modifications to the predictive likelihood equations in order to find such predictors. We compute their mean square prediction errors by simulation and compare them with the best linear unbiased predictors and alternative linear unbiased predictors for n = 5 and 10 and for selected r and s values. A modification based on first-order Taylor series expansion applied in a two-step procedure appears to yield good predictors when s > r + 1. (C) 1997 Elsevier Science B.V.