LAUSR

We investigate the estimation of high-dimensional normal mean under sparsity. Most shrinkage priors in the literature are based on certain assumptions of sparsity levels and signal sizes. Violation of these assumptions can lead to unsatisfactory estimation. In this paper, we propose a new class of flexible priors, the adaptive normal-hypergeometric-inverted-Beta (ANHIB) priors, which generalize several popular shrinkage priors without requiring prior knowledge of data sparsity levels and signal sizes, and thus can be used as good default priors in a large variety of situations. We show that the ANHIB estimators provide strong suppression to noises and little shrinkage to large signals, and have consistently superior estimation performance under various sparsity levels and signal sizes.