A MINIMUM DISCRIMINATION INFORMATION ESTIMATOR OF PRELIMINARY CONJECTURED NORMAL VARIANCE

D. V. GOKHALE^{1}, KOICHI INADA^{2} AND HEA-JUNG KIM^{3}

1Department of Statistics, University of California, Riverside, CA 92521-0138, U.S.A.

2Department of Mathematics, Kagoshima University, Kagoshima 890, Japan 3Department of Statistics, Dongguk University, Seoul 100-715, Korea

(Received July 25, 1991; revised June 10, 1992)

Abstract. For the problem of estimating the normal variance σ^{2} based on random sample X_{1}, …, X_{n} when a preliminary conjectured interval [C_{0}^{−1}σ_{0}^{2}, C_{0}σ_{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.

Key words and phrases: Minimum discrimination information, Kullback-Leibler discrimination information measure, preliminary conjecture, preliminary test, minimax criterion, mean square error efficiency.