 
Summary: Statistics & Probability Letters 70 (2004) 8794
Shrinkage estimation for convex polyhedral cones
Anna AmirdjanovaÃ, Michael Woodroofe
Department of Statistics, The University of Michigan, 455 West Hall, 550 E University, Ann Arbor, MI 481091092, USA
Abstract
Estimation of a multivariate normal mean is considered when the latter is known to belong to a convex
polyhedron. It is shown that shrinking the maximum likelihood estimator towards an appropriate target
can reduce mean squared error. The proof combines an unbiased estimator of a risk difference with some
geometrical considerations. When applied to the monotone regression problem, the main result shows that
shrinking the maximum likelihood estimator towards modifications that have been suggested to alleviate
the spiking problem can reduce mean squared error.
r 2004 Elsevier B.V. All rights reserved.
Keywords: Degrees of freedom; Maximum likelihood estimator; Mean squared error; Primaldual bases; Projections;
Stein's Identity; Target estimator
1. Introduction
Let y ¼ ðy1; . . . ; ynÞ0
denote a normally distributed random vector with unknown mean y and
covariance matrix s2
In and suppose that y is known to belong to a closed convex polyhedron
O Rn
