Orateur: Pascaline Descloux
Titre: Stein's phenomenon and shrinkage estimators
Résumé: In estimation theory, Stein (1956) and James, Stein (1961) proved that in the simple problem of simultaneously estimating the means of p independent normal random variables, the usual and most intuitive estimator is inadmissible when p>2. The idea underlying their result, namely the use of shrinkage to reduce the variance of the usual estimator, had a huge impact on the development of statistical methodology. In this talk I will prove that the James-Stein estimator dominates the usual one, thereby proving the inadmissibility of the latter. I will then illustrate the benefits of shrinkage estimators in linear regression through the example of ridge regression.

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