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Statistics Seminar

Improved performance guarantees for Tukey’s median

With Stanislav Minsker (University of Southern California)

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.

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