CONDITIONAL PROPERTIES OF BAYESIAN INTERVAL ESTIMATES

ANNA NICOLAOU

Economic and Social Sciences, University of Macedonia, Egnatia str. 156, P.O. Box 1591, 54006 Thessaloniki, Greece

(Received April 13, 1992; revised March 23, 1993)

Abstract. Consider the construction of an interval estimate for a scalar parameter of interest in the presence of orthogonal nuisance parameters. A conditional prior density on the parameter of interest that is proportional to the square root of its information element, generates one-sided Bayes intervals that are approximately confidence intervals as well, having coverage error of order O(1/n), where n is the sample size. We show that the frequency property of these intervals also holds conditionally on a locally ancillary statistic near the true parameter value.

Key words and phrases: Bayes intervals, nuisance parameters, orthogonal parameters, local ancillarity.