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Concentration of measure for radial distributions and consequences for statistical modeling

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  • Arias-Castro, Ery
  • Pu, Xiao

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.

Suggested Citation

  • Arias-Castro, Ery & Pu, Xiao, 2019. "Concentration of measure for radial distributions and consequences for statistical modeling," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 216-223.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:216-223
    DOI: 10.1016/j.spl.2018.09.016
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    References listed on IDEAS

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    1. Chang, George T. & Walther, Guenther, 2007. "Clustering with mixtures of log-concave distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6242-6251, August.
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