Concentration of measure for radial distributions and consequences for statistical modeling

Ery Arias-Castro and Xiao Pu

Statistics & Probability Letters, 2019, vol. 145, issue C, 216-223

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: Concentration of measure; Radial distribution; High-dimensional; Statistical modeling (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.09.016

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