Shrinkage estimation for convex polyhedral cones

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.