Concentration of measure for radial distributions and consequences for statistical modeling

Publication date: Available online 9 October 2018Source: Statistics & Probability LettersAuthor(s): Ery Arias-Castro, Xiao PuAbstractMotivated 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.

Source: Statistics and Probability Letters - October 10, 2018 Category: Statistics Source Type: research