Invariant Empirical Bayes Confidence Interval for Mean Vector of Normal Distribution and its Generalization for Exponential Family

Abstract

Based on a given Bayesian model of multivariate normal with known variance matrix we will find an empirical Bayes confidence interval for the mean vector components which have normal distribution. We will find this empirical Bayes confidence interval as a conditional form on ancillary statistic. In both cases (i.e. conditional and unconditional empirical Bayes confidence interval), the empirical Bayes confidence interval is invariant w.r.t. the group with given confidence level. Finally the problem can be generalized for the exponential family.

Keywords

• empirical bayes
• bayes estimator
• invariant confidence interval