Shrinkage: Stein's Paradox by Henry Walsh '23, Statistics Colloquium

Shrinkage: Stein’s Paradox by Henry Walsh ’23, Statistics Colloquium, Wednesday, April 26, 1:10 – 1:50 pm, North Science Building 114, Wachenheim.

Abstract:  To start, I will talk a little bit about x bar, the average of a sample, and a few of the useful things it can do.  Then, I will mention how when there are multiple samples, each individual average shrinks toward the grand average, and that by including this bias in our predictions of each individual mean, our predictions are, on average, always better, no matter what the true grand mean is.  This is all independent of what averages we are taking, as they could be entirely different measurements or units and this idea still holds up.  I will then prove this fact, Stein’s lemma, follow it up with a connection to some Bayesian ideas of estimating an unknown mean, and end with an example using baseball batting averages.