|
Abstract:
|
Charles Stein stunned the statistical world in the 1950s by proving, when estimating three or more independent component means with Normal distributions, that the sample mean vector is inadmissible. That assumed a risk function based on aggregated quadratic component losses with each component weighted inversely to its variance. His improved estimators, including the now celebrated "James-Stein estimator", were based on shrinkage factors that allow exact calculations even for small samples. Over the years his ingenious and paradoxical result based on shrinkage ideas has led statisticians vigorously to pursue new theory and generalizations that have greatly benefited statistical practice. Extensions include allowing more general loss functions, using exchangeability assumptions to avoid dependence on loss function weights, non-Normal distributions, interval estimates, proper Bayes procedures and improper objective Bayes procedures.
Charles Stein, was a recognized creative genius in mathematical statistics, and a remarkable human being.
|
