Equivariant Estimation in a Model with an Ancillary Statistic

Abstract

This paper reformulates a result of Hora and Buehler on best equivariant estimators to treat a model admitting an ancillary statistic. The approach itself was established by Pitman, Girshick and Savage and Kiefer, and expanded by Zidek. The model considered in this paper is assumed to be generated as an orbit under a group acting on the parameter space. The general result obtained here is applied to a model in the Nile problem, a model with a known variation coefficient, a circle model and the GMANOVA model, and best equivariant estimators (BEE's) are derived. In the first two models, the BEE's dominate the MLE's uniformly.