Concentration of Measure for Radial Distributions and Consequences for Statistical Modeling
Statistics Theory
2016-09-13 v2 Statistics Theory
Abstract
Motivated by problems in high-dimensional statistics such as mixture modeling for classification and clustering, we consider the behavior of radial densities as the dimension increases. We establish a form of concentration of measure, and even a convergence in distribution, under additional assumptions. This extends the well-known behavior of the normal distribution (its concentration around the sphere of radius square-root of the dimension) to other radial densities. We draw some possible consequences for statistical modeling in high-dimensions, including a possible universality property of Gaussian mixtures.
Keywords
Cite
@article{arxiv.1607.07549,
title = {Concentration of Measure for Radial Distributions and Consequences for Statistical Modeling},
author = {Ery Arias-Castro and Xiao Pu},
journal= {arXiv preprint arXiv:1607.07549},
year = {2016}
}