Joint Linear Estimation and Prediction Based on Order Statistics in a Linear Model

With reference to a censored sample in a linear model setup, where the underlying distribution belongs to the location-scale family, we investigate inference problems on unobserved order statistics on the basis of the observed ones. Results are obtained on optimal joint prediction as well as joint estimation in the Loewner order sense. The derivation here is considerably more intricate than that in related earlier work in the iid context. Practically motivated illustrative examples are also given and discussed.