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CONDITIONAL PROPERTIES OF BAYESIAN

INTERVAL ESTIMATES

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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.

**Source**
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