COVERAGE PROPERTIES OF ONE-SIDED INTERVALS IN THE DISCRETE CASE AND APPLICATION TO MATCHING PRIORS

JUDITH ROUSSEAU

Laboratoire de Statistique, CREST, Timbre J340, 92241 Malakoff Cedex, France and Laboratoire de Statistique Théorique et Appliquée, Université de Paris 6, France

(Received September 22, 1997; revised August 14, 1998)

Abstract. We consider asymptotic coverage properties of one-sided posterior confidence intervals for discrete distributions, with a unidimensional parameter of interest and a nuisance parameter of arbitrary dimension. In this case, no higher order asymptotic expansion of the frequentist coverage for these intervals is established, unless some randomization is added. We study here the existence of such frequentist expansions and propose simple continuity corrections based on a uniform random vector. This helps in determinig a family of matching priors for one sided intervals in the discrete case.

Key words and phrases: Asymptotic expansion, credible region, Edgeworth expansion, frequentist coverage, lattice distribution, posterior coverage.