Improved estimates of location in the presence of an unknown scale

AbstractWe investigate conditions under which estimators of the form X + aU′Ug(X) dominate X when X, a p × 1 vector, and U, an m × 1 vector, are distributed such that [X1, X2,…, Xp, U1, U2,…, Up]′σ has a spherically symmetric distribution about [θ1, θ2,…, θp, 0, 0,…, 0]′, where σ is an unknown scale. Brandwein and Strawderman [2] have results for quadratic loss and we extend these results to concave functions of quadratic loss and to general quadratic loss