|Stochastic Systems Group|
In 1961, James and Stein introduced an estimator of the mean of a multivariate normal distribution that achieves a smaller mean-squared error than the maximum likelihood estimator in dimensions three and higher. This estimator shrinks the observation vector toward a previously specified point target by an adaptive shrinkage factor. I discuss the properties of the James-Stein estimator and describe how it can be adapted to various settings. I examine its application to the problems of dynamic state estimation and function denoising as presented in two recent papers, and discuss an extension of the estimator to the scenario in which specification of a single point shrinkage target is impractical. This talk is based on my area exam.
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