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Stein's Paradox

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Stein’s paradox is one of the most surprising results in Statistics. Suppose X1,...,Xp are independent random variables, with Xi ~ N(θi,1). If we want to estimate θ = (θ1,...,θp), the most obvious choice is to use X = (X1,...,Xp). It turns out that, provided p>2, we can find a better estimator, in a very natural sense that I will make precise. As well as giving the (fairly straightforward) proof, I will discuss geometric intuition and other explanations for this result, and discuss extensions. I will also show how the improved estimator can be used to give good predictions of baseball batting averages.

This talk is part of the The Archimedeans (CU Mathematical Society) series.

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