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

[摘要] We consider the problem of estimating the mean vector theta of a d-dimensional spherically symmetric distributed X based on balanced loss functions of the forms: (i) omega rho(parallel to delta - delta(0)parallel to(2)) + (1 - omega)rho(parallel to delta - theta parallel to(2)) and (ii) l(omega parallel to delta - delta(0)parallel to(2) + (1 - omega)parallel to delta - theta parallel to(2)), where delta(0) is a target estimator, and where rho and l are increasing and concave functions. For d >= 4 and the target estimator delta(0)(X) = X, we provide Baranchik-type estimators that dominate delta(0)(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 rho' and l'. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] Balanced loss;Concave loss;Dominance;Kotz distribution;Shrinkage estimation;Spherically symmetric