A SHRINKAGE ESTIMATOR OF THE BIVARIATE NORMAL MEAN WITH INTERVAL RESTRICTIONS

Abstract

This study is concerned with estimating the bivariate normal mean vector (ƒÊ = (ƒÊi ƒÊ2)•Œ) for the case where one has a prior information about the mean vector in the form of preliminary conjectured intervals, ƒÊi • ̧ [ƒÉi ƒÂi, ƒÉi + ƒÂi], for ƒÂi > 0, i = 1, 2. It is based on the minimum discrimination information(MDI) approach, intended to propose and develop an estimator that has lower risk than a usual estimator (m.l.e.) in or beyond the conjectured intervals. The MDI estimator is obtained for the constrained estimation. This yields a shrinkage type estimator that shrinks towards the preliminary conjectured intervals. Its risk is evaluated and compared with the usual estimator under a quadratic loss function. Favorable properties of the proposed estimator are noted and recommendations for its use are also made.