A Note on Decision Theoretic Estimation of
Ordered Parameters
George Iliopoulos
This paper deals with decision theoretic estimation of the middle among
three ordered location parameters under an arbitrary strictly convex loss
function. Double shrinkage estimators are produced which use all the available
data and improve on single shrinkage ones. The case of estimation of the middle
among three ordered scale parameters with possible existence of nuisance parameters
is also discussed.
AMS 1991 subject classifications: 62C15, 62F10, 62F30
Key words and phrases: Decision theory, ordered location and scale
parameters, convex loss function, shrinkage estimation.