2021/02/25 by Lahoucine Hobbad, Hobbad, Lahoucine, Éric Marchand +3
Computer Science · Mathematics · #62C15 #62C20 (Secondary) #62F10 (Primary) #62J07 #Bayesian Methods and Mixture Models #FOS: Mathematics #Mathematical Approximation and Integration #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62C15 #msc:62C20 #msc:62F10 #msc:62J07 #stat.TH
paper · pdf · doi:10.48550/arxiv.2102.13083
arxiv created 2021/02/25 · openalex publication_date 2021/02/25 · arxiv updated 2021/02/26 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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: \bf (i) ωρ(‖\de-\de0‖2) +(1-ω)ρ(‖\de - θ‖2) and \bf (ii) ℓ(ω‖\de - \de0‖2 +(1-ω)‖\de - 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 (\citems2020) in two directions: \bf (a) from scale mixture of normals to the spherical class of distributions with Lebesgue densities and \bf (b) from completely monotone to concave ρ' and ℓ'.