Showing papers by "William E. Strawderman published in 2019"

On shrinkage estimation for balanced loss functions

Abstract: The estimation of a multivariate mean $\theta$ is considered under natural modifications of balanced loss function of the form: (i) $\omega \, \rho(\|\delta-\delta_0\|^2) + (1-\omega) \, \rho(\|\delta-\theta\|^2) $, and (ii) $\ell \left( \omega \, \|\delta-\delta_0\|^2 + (1-\omega) \, \|\delta-\theta\|^2 \right)\,$, where $\delta_0$ is a target estimator of $\gamma(\theta)$. After briefly reviewing known results for original balanced loss with identity $\rho$ or $\ell$, we provide, for increasing and concave $\rho$ and $\ell$ which also satisfy a completely monotone property, Baranchik-type estimators of $\theta$ which dominate the benchmark $\delta_0(X)=X$ 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 $\rho$ or $\ell

On An Intriguing Distributional Identity

Abstract: For a continuous random variable X with support equal to (a, b), with c.d.f. F, and g: Ω1 → Ω2 a continuous, strictly increasing function, such that Ω1∩Ω2⊇(a, b), but otherwise arbitrary, we establish that the random variables F(X) − F(g(X)) and F(g− 1(X)) − F(X) have the same distribution. Further developments, accompanied by illustrations and observations, address as well the equidistribution identity U − ψ(U) = dψ− 1(U) − U for U ∼ U(0, 1), where ψ is a continuous, strictly increasing and onto function, but otherwise arbitrary. Finally, we expand on applications with connections to variance reduction techniques, the discrepancy between distributions, and a risk identity in predictive density estimation.