FREQUENTIST VALIDITY OF HIGHEST POSTERIOR DENSITY REGIONS IN THE MULTIPARAMETER CASE

J. K. GHOSH^{1} AND RAHUL MUKERJEE^{2,}

1Stat-Math Division, Indian Statistical Institute, 203, B. T. Road, Calcutta 700 035, India

2Indian 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-inform-ative prior, parametric orthogonality.