COMPLETE CLASSES OF TESTS FOR REGULARLY VARYING DISTRIBUTIONS

JACEK P. KOWALSKI

TRC, Department of Applied Mathematics, University of Adelaide, Adelaide 5005, Australia

(Received March 8, 1994; revised July 27, 1994)

Abstract. This paper establishes essentially complete class theorems and gives conditions for admissibility of tests for parametric families of distributions having some kinds of regular variation properties. A complete treatment of topologically contiguous one-dimensional bounded and unbounded hypotheses is given. Examples of applications to well known families of distributions are presented.

Key words and phrases: Essentially complete class, admissibility, Bayes test, regular variation.