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On Minimax Shrinkage Estimation with Variable Selection

In: Robust and Multivariate Statistical Methods

Author

Listed:
  • Stavros Zinonos

    (RWJMS, Cardiovascular Institute of New Jersey)

  • William E. Strawderman

    (Rutgers University, Department of Statistics and Biostatistics)

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.

Suggested Citation

  • Stavros Zinonos & William E. Strawderman, 2023. "On Minimax Shrinkage Estimation with Variable Selection," Springer Books, in: Mengxi Yi & Klaus Nordhausen (ed.), Robust and Multivariate Statistical Methods, pages 65-86, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-22687-8_4
    DOI: 10.1007/978-3-031-22687-8_4
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