La paradoja de Stein

Abstract

[en] The (population) mean of a $p$-dimensional multivariate normal vector is plainly estimated by the empirical mean which, additionally, is minimax, ML, UMV and least squares BLUE. One would fancy it is also best as to risk. Nonetheless, Stein (1956) proved it is inadmissible for $p>2$, showing alternative, better candidates. This is Stein's paradox, origin of this memoir.

We begin with a brief introduction to place Stein's result in its proper historical context. Then, after reviewing some basic Statistics concepts we present Stein's result, accompanied by illustrative simulations. Finally we survey several approaches to understanding the paradox.