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Activity Number: 370 - A Memorial Session for Arthur Cohen
Type: Invited
Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
Sponsor: Memorial
Abstract #320965
Title: On Minimax Shrinkage Estimation with Variable Selection
Author(s): Willliam Edward Strawderman*
Companies: Rutgers University
Keywords: variable selection; minimaxity; quadratic loss
Abstract:

We study minimax estimators of the mean vector of a spherically symmetric distribution that also perform variable selection by estimating certain components as 0. The basic class of estimators developed is closely related to, and generalizes, classes considered by Zhou and Hwang and Maruyama in the Gaussian setting. The class of distributions studied includes scale mixtures of normals (including Normal and Student-t) as well as the general class of spherically symmetric distributions with a residual vector. Certain subclasses of these estimators based on truncated order statistics are shown to be particularly effective when some information on the sparsity is known.


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