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Metric entropy of high dimensional distributions


Authors: Ron Blei, Fuchang Gao and Wenbo V. Li
Journal: Proc. Amer. Math. Soc. 135 (2007), 4009-4018
MSC (2000): Primary 60G15, 46B50.
DOI: https://doi.org/10.1090/S0002-9939-07-08935-6
Published electronically: September 7, 2007
MathSciNet review: 2341952
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Abstract: Let $ \mathcal F_d$ be the collection of all $ d$-dimensional probability distribution functions on $ [0,1]^d$, $ d\ge 2$. The metric entropy of $ \mathcal F_d$ under the $ L_2([0,1]^d)$ norm is studied. The exact rate is obtained for $ d=1,2$ and bounds are given for $ d>3$. Connections with small deviation probability for Brownian sheets under the sup-norm are established.

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Additional Information

Ron Blei
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06268
Email: blei@math.uconn.edu

Fuchang Gao
Affiliation: Department of Mathematics, University of Idaho, Moscow, Idaho 83844
Email: fuchang@uidaho.edu

Wenbo V. Li
Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
Email: wli@math.udel.edu

DOI: https://doi.org/10.1090/S0002-9939-07-08935-6
Received by editor(s): May 23, 2006
Received by editor(s) in revised form: August 25, 2006, and September 19, 2006
Published electronically: September 7, 2007
Additional Notes: The first author was supported in part by NSF Grant DMS-0405855.
The second author was supported in part by NSF Grant DMS-0505805.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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