Moment properties of estimators for an extreme value regression model with type 2 censoring

Abstract

An extreme value regression model for grouped data with type 2 censoring is considered. The response variable is taken to have a type 1 ext reme va lue d i s t r i b u t i on for sma l l e s t v a l ue s a nd a s tandar d linear regression model is assumed f o r t he means . Large sampl e approximations to the variances of the maximum likelihood estimators are derived. The small sample moment properties of the maximum likelihood estimators are evaluated by simulation for the case of simp l e l i n e a r r e g ress i o n . T h e r e sul t s s h o w t h a t t h e e stima t or o f the scale parameter has a s t rong bias in sma l l samples, particularly when ther e is a heavy degree of censoring. Final l y , sma l l sample variance and mean square error efficiences of the best linear unbiased estimators relative to the maximum likelihood estimators are assessed.