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) |
|---|---|
| Article number | 104558 |
| Journal | Journal of Multivariate Analysis |
| Volume | 175 |
| DOIs | |
| State | Published - Jan 2020 |
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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
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On shrinkage estimation for balanced loss functions. / Marchand, Éric; Strawderman, William E.
In: Journal of Multivariate Analysis, Vol. 175, 104558, 01.2020.Research output: Contribution to journal › Article
TY - JOUR
T1 - On shrinkage estimation for balanced loss functions
AU - Marchand, Éric
AU - Strawderman, William E.
PY - 2020/1
Y1 - 2020/1
N2 - 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.
AB - 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.
KW - Balanced loss
KW - Concave loss
KW - Dominance
KW - Multivariate normal
KW - Scale mixture of normals
KW - Shrinkage estimation
UR - http://www.scopus.com/inward/record.url?scp=85073258500&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85073258500&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2019.104558
DO - 10.1016/j.jmva.2019.104558
M3 - Article
AN - SCOPUS:85073258500
VL - 175
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
M1 - 104558
ER -