Geometric Methods for Nonparametric Inference: The Curious Case of Dimension 8

Seminar in Mathematics

Abstract: Random geometric graphs play a central role in the construction of many popular multivariate non-parametric statistical tests. These include, among several others, the celebrated Friedman-Rafsky two-sample test based on the minimal spanning tree, the Bickel-Breiman spacings tests for goodness-of-fit, and recent methods for independence testing based on nearest-neighbors graphs. In this talk, using the tools from geometric probability, we will present various results on the asymptotic properties of these tests. Several interesting properties will emerge, such as a curious phase transition in dimension 8, which appears to be related to the geometry of Euclidean interpoint distances.