A minimum discrimination information estimator of preliminary conjectured normal variance

For the problem of estimating the normal variance ² based on random sampleX ₁,...,X _n when a preliminary conjectured interval C ₀ ^–1 ₀ ² ,C _{0 0} ² ] is available, the minimum discrimination information (MDI) approach is presented. This provides a simple way of specifying the prior information, and also allows to consider a shrinkage type estimator. MDI estimator and its mean square error are derived. The estimator compares favorably with the previously proposed estimators in terms of mean square error efficiency.