Abstract

The question of recovering a multiband signal from noisy observations motivates a model in which the multivariate data points consist of an unknown deterministic trend # observed with multivariate Gaussian errors. A cognate random trend model suggests affine shrinkage estimators #A and #B for #, which are related to an extended Efron-Morris estimator. When represented canonically, #A performs componentwise James-Stein shrinkage in a coordinate system that is determined by the data. Under the original deterministic trend model, #A and its relatives are asymptotically minimax in Pinsker's sense over certain classes of subsets of the parameter space. In such fashion, #A and its cousins dominate the classically efficient least squares estimator. We illustrate their use to improve on the least squares fit of the multivariate linear model.

Citations