earticle

영어

Consider the problem of estimating a p X 1 mean vector θ (p-q ≥ 3), q = rank(Pv) with a projection matrix Pv under the quadratic loss, based on a sample X1, X2, ㆍㆍㆍ, Xn. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ∥θ - Pvθ∥ is restricted to a known interval, where Pv is an idempotent and projection matrix and rank(Pv) = q. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.