Abstract
The estimation of a multivariate mean θ is considered under natural modifications of balanced loss functions of the form: (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 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 language | English (US) |
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Article number | 104558 |
Journal | Journal of Multivariate Analysis |
Volume | 175 |
DOIs | |
State | Published - Jan 2020 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty
Keywords
- Balanced loss
- Concave loss
- Dominance
- Multivariate normal
- Scale mixture of normals
- Shrinkage estimation