The local geometry of finite mixtures

Gassiat, Elisabeth; van Handel, Ramon

doi:10.1090/S0002-9947-2013-06041-2

The local geometry of finite mixtures
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by Elisabeth Gassiat and Ramon van Handel PDF

Trans. Amer. Math. Soc. 366 (2014), 1047-1072 Request permission

Abstract:

We establish that for $q\ge 1$, the class of convex combinations of $q$ translates of a smooth probability density has local doubling dimension proportional to $q$. The key difficulty in the proof is to control the local geometric structure of mixture classes. Our local geometry theorem yields a bound on the (bracketing) metric entropy of a class of normalized densities, from which a local entropy bound is deduced by a general slicing procedure.

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