On shrinkage estimation for balanced loss functions

Éric Marchand, William E. Strawderman

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The estimation of a multivariate mean θ is considered under natural modifications of balanced loss functions of the form: (i) ωρ(‖δ−δ02)+(1−ω)ρ(‖δ−θ‖2), and (ii) ℓω‖δ−δ02+(1−ω)‖δ−θ‖2, where δ0 is a target estimator of γ(θ). After briefly reviewing known results for original balanced loss with identity ρ or ℓ, we provide, for increasing and concave ρ and ℓ which also satisfy a completely monotone property, Baranchik-type estimators of θ which dominate the benchmark δ0(X)=X for X either distributed as multivariate normal or as a scale mixture of normals. Implications are given with respect to model robustness and simultaneous dominance with respect to either ρ or ℓ.

Original languageEnglish (US)
Article number104558
JournalJournal of Multivariate Analysis
StatePublished - Jan 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


  • Balanced loss
  • Concave loss
  • Dominance
  • Multivariate normal
  • Scale mixture of normals
  • Shrinkage estimation


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