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. Our derivation proceeds in a direct way that avoids the algebraically heavy Lagrangian multiplier employed in related earlier work in non-regression context. The results are finally illustrated with an example.