The local geometry of finite mixtures

. 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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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2014-02, Vol.366 (2), p.1047-1072
Main Authors: GASSIAT, ELISABETH, VAN HANDEL, RAMON
Format: Article
Language:English
Subjects:
Density
Entropy
Fourier transformations
Geometry
Mathematical constants
Mathematical lattices
Mathematical theorems
Polynomials
Probabilities
Series convergence
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Description
Summary:. 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.]]>
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2013-06041-2