Lecture

The Stein Phenomenon and Superefficiency

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In course

MATH-442: Statistical theory

This course gives a mostly rigourous treatment of some statistical methods outside the context of standard likelihood theory. ...

Description

This lecture delves into the Stein Phenomenon, where the James-Stein Estimator dominates the Maximum Likelihood Estimator (MLE) in Gaussian estimation under quadratic loss. It challenges the belief in the MLE's universal optimality, showcasing the benefits of bias in high-dimensional statistics. The lecture also covers Hodges' Superefficient Estimator, highlighting its superiority over the MLE in certain scenarios. The discussion extends to asymptotic optimality, asymptotically Gaussian estimators, and the Cramér-Rao bound. Through examples and proofs, the lecture explores the intricacies of estimation theory, emphasizing the importance of regular sequences of estimators and the implications of superefficiency.

Instructor

Yoav Zemel

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

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