Abstract

We consider the problem of estimating a high-dimensional vector of parameters from a noisy one-time observation. The noise is iid Gaussian with known variance, and the performance of the estimator is measured via squared-error loss. For this problem, shrinkage estimators, which shrink the observed data towards a point or a target subspace, have been popular because they dominate the simple maximum-likelihood estimator (when the number of dimensions exceeds two). In this talk, we review the key aspects of shrinkage estimation, and then introduce shrinkage estimators that use the data to determine a “good” target subspace to shrink the data towards. We give concentration results for the squared-error loss and convergence results for the risk of the proposed estimators. We also present simulation results that validate the theory.