A SHRINKAGE ESTIMATOR OF THE BIVARIATE NORMAL MEAN WITH INTERVAL RESTRICTIONS

This study is concerned with estimating the bivariate normal mean vector (μ= (μ_1 μ_2)') for the case where one has a prior information about the mean vector in the form of preliminary conjectured intervals, μ_i ∈ [λ_i-δ_i, λ_i+δ_i], for δ_i > 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 recommendationts for its use are also made.