On Minimax Shrinkage Estimation with Variable Selection

Stavros Zinonos () and William E. Strawderman ()
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Stavros Zinonos: RWJMS, Cardiovascular Institute of New Jersey
William E. Strawderman: Rutgers University, Department of Statistics and Biostatistics

A chapter in Robust and Multivariate Statistical Methods, 2023, pp 65-86 from Springer

Abstract: 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 (2005) and Maruyama (2014) in the Gaussian setting. The class of distributions studied includes scale mixtures of normals (e.g., 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.

Keywords: Shrinkage estimation; Variable selection; Minimaxity; Quadratic loss (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-22687-8_4

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DOI: 10.1007/978-3-031-22687-8_4

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