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arXiv · 1607.07549

Concentration of Measure for Radial Distributions and Consequences for Statistical Modeling

Ery Arias-Castro·Xiao Pu
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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.

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Ery Arias-Castro, Xiao Pu. 2016-07-26. Concentration of Measure for Radial Distributions and Consequences for Statistical Modeling. https://arxiv.org/abs/1607.07549

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