A0312
Title: Improved performance guarantees for Tukey's median
Authors: Stanislav Minsker - University of Southern California (United States)
Yinan Shen - University of Southern California (United States) [presenting]
Abstract: Improved performance guarantees are presented for empirical Tukey's median, the deepest point associated with the given sample when the data generating distribution is elliptically symmetric and possibly anisotropic. Some of the results remain valid in the wider class of affine equivariant estimators. As a corollary of the bounds, it is shown that the diameter of the set of all empirical Tukey's medians scales like $o(1/sqrt{n})$ where n is the sample size. Moreover, when the data are 2-dimensional, it is proven that the diameter is of order $O(n^3/4 log3/2(n))$.
