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Submitted by pscully on Fri, 04/23/2010 - 16:46.
04/29/2010 - 16:10
04/29/2010 - 17:30
STA/BST 290: Rudy Beran (UC Davis)
The Unbearable Transparency of Stein Estimation
Thursday, April 29th, 2010 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)
Speaker: Rudy Beran (Statistics, UC Davis)
Title: The Unbearable Transparency of Stein Estimation
Abstract: In the first half of the nineteenth century, Gauss offered two arguments to support least squares estimators: first, the reasoning now called maximum likelihood estimation; second, in a letter to Bessel, the concept of risk and the seed of the Gauss-Markov theorem.
Charles Stein (1956) discovered that the least squares estimator for a mean vector that is observed once, with independent standard normal errors, is inadmissible under quadratic risk if the dimension of the mean vector exceeds two.
It has since been claimed that Stein's result is counter-intuitive, even paradoxical, and is not very useful. In response to assertions of paradox, Efron and Morris (1973) presented an alternative empirical Bayes approach to Stein estimation. Stigler (1990) gave another derivation based on a "Galtonian perspective". But surely Stein himself did not find his results paradoxical. Is it not more likely that assertions of "paradoxical" or "counter-intuitive" or "useless" have overlooked essential discussions in Stein's brilliant 1956 paper?
This talk will elaborate on three such arguments from the paper: the asymptotic geometry of quadratic loss in high dimensions that makes Stein estimation transparent, the orthogonal equivariance reasoning that suffices to establish Pinsker-type (1980) asymptotic minimaxity for the James-Stein estimator, and the use of multiple shrinkage to obtain practically effective estimators.