FREQUENTIST VALIDITY OF HIGHEST POSTERIOR DENSITY
REGIONS IN THE MULTIPARAMETER CASE

J. K. GHOSH1 AND RAHUL MKERJEE2

1 Stat-Math Division, Indian Statistical Institute, 203, B. T. Road, Calcutta 700 035, India
2 Indian Institute of Management, Joka, Diamond Harbour Road, Post Box No. 16757,
Alipore Post Office, Calcutta 700 027, India

(Received June 1, 1991; revised November 16, 1991)

Abstract.    In a multiparameter set-up, this paper characterizes priors which ensure frequentist validity, up to o(n-1), of confidence regions based on the highest posterior density. The role of Jeffreys' prior in this regard has also been investigated.

Key words and phrases:    Highest posterior density, Jeffreys' prior, non-informative prior, parametric orthogonality.

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