Séminaire de Probabilités et Statistique :
Le 26 mai 2025 à 13:45 - UM - Bât 09 - Salle de conférence (1er étage)
Présentée par Minsker Stanislav - University of Southern California (USC Dornsife)
Improved performance guarantees for Tukey’s median
Is there a natural way to order data in dimension greater than one? The approach based on the notion of half-space depth, often associated with the name of John Tukey, is among the most popular. Tukey’s depth has found applications in robust statistics, the study of elections and social choice, and graph theory. We will give an introduction to the topic, with an emphasis on robust statistics, describe some remaining open questions as well as our recent progress towards their solutions. In will particular, we discuss performance guarantees for Tukey’s median (and other affine-equivariant estimators) that depend on the “intrinsic” dimension of the problem expressed via the effective rank of the covariance matrix, and their connections to the size of empirical depth level sets.
This talk is based on the joint work with Yinan Shen.
Séminaire en salle 109, également retransmis sur zoom : https://umontpellier-fr.zoom.us/j/7156708132