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On shrinkage estimation of a spherically symmetric distribution for balanced loss functions

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  • Hobbad, Lahoucine
  • Marchand, Éric
  • Ouassou, Idir

Abstract

We consider the problem of estimating the mean vector θ of a d-dimensional spherically symmetric distributed X based on balanced loss functions of the forms: (i) ωρ(‖δ−δ0‖2)+(1−ω)ρ(‖δ−θ‖2) and (ii) ℓω‖δ−δ0‖2+(1−ω)‖δ−θ‖2, where δ0 is a target estimator, and where ρ and ℓ are increasing and concave functions. For d≥4 and the target estimator δ0(X)=X, we provide Baranchik-type estimators that dominate δ0(X)=X and are minimax. The findings represent extensions of those of Marchand & Strawderman (2020) in two directions: (a) from scale mixture of normals to the spherical class of distributions with Lebesgue densities, and (b) from completely monotone to concave ρ′ and ℓ′.

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  • Hobbad, Lahoucine & Marchand, Éric & Ouassou, Idir, 2021. "On shrinkage estimation of a spherically symmetric distribution for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jmvana:v:186:y:2021:i:c:s0047259x21000725
    DOI: 10.1016/j.jmva.2021.104794
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    References listed on IDEAS

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    1. Jafari Jozani, Mohammad & Marchand, Éric & Parsian, Ahmad, 2006. "On estimation with weighted balanced-type loss function," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 773-780, April.
    2. Dey, Dipak K. & Ghosh, Malay & Strawderman, William E., 1999. "On estimation with balanced loss functions," Statistics & Probability Letters, Elsevier, vol. 45(2), pages 97-101, November.
    3. Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2012. "Bayesian and Robust Bayesian analysis under a general class of balanced loss functions," Statistical Papers, Springer, vol. 53(1), pages 51-60, February.
    4. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
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