Tel-Aviv University
School of Mathematical Sciences

Department Colloquium


Monday, May 16, 2016

Holcblat hall 007, 12:15



Lucien Birgé


Universite Pierre et Marie Curie


 Universal estimators - maximum likelihood and beyond



Abstract:
One major problem in Statistics is (in its simplest form) the following: given n  i.i.d. random variables X1, . . . , Xn with a common unknown distribution P and the assumption that P  belongs to some given family 𝒫 of probabilities, use the Xi to guess P 𝒫 .
In the 20ís, Ronald Fisher invented and popularized the Maximum Likelihood method which has been considered for a long time and by many people as some sort of a universal estimator. Its properties have been studied at length but it was also discovered that it suffered from various weaknesses.
I shall explain the method and show why it may or may not work, point out some major deficiencies, then explain how to replace it by an alternative solution, based on notions related to metric entropy and robustness, that substantially improves on the Maximum Likelihood, at least from a theoretical point of view.



Coffee will be served at 12:00 before the lecture
near Holcblat hall 007