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On efficient prediction and predictive density estimation for normal and spherically symmetric models

Banff International Research Station for Mathematical Innovation and Discovery

Let $X ~ Nd(q,s2I)$, $Y ~ Nd(q, s2I)$, $U ~ Nk(q, s2I)$ be independently distributed, or more generally let $(X, Y, U)$ have a spherically symmetric distribution with density $hd+k/2f (h(||x â q||2+ ||u||2+ ||y â cq||2))$ with unknown parameters $h \in Rd$, and with known density $f( . )$ and constant $c > 0$. Based on observing $X = x, U = u$, we consider the problem of obtaining a predictive density $q_hat( â ¢ ; x, u)$ for $Y$ with risk measured by the expected Kullbackâ Leibler loss. A benchmark procedure is the minimum risk equivariant density $

Mathematics; Statistics

video/mp4

Author affiliation: Rutgers University

2019-10-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71834

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/