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Metric entropy of high dimensional distributions

Author(s): Ron Blei; Fuchang Gao; Wenbo V. Li
Journal: Proc. Amer. Math. Soc. 135 (2007), 4009-4018.
MSC (2000): Primary 60G15, 46B50.
Posted: September 7, 2007
MathSciNet review: 2341952
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Abstract | References | Similar articles | Additional information

Abstract: Let $\mathcal F_d$ be the collection of all -dimensional probability distribution functions on , $d\ge 2$ . The metric entropy of $\mathcal F_d$ under the norm is studied. The exact rate is obtained for and bounds are given for . Connections with small deviation probability for Brownian sheets under the sup-norm are established.

References:

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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: 10.1090/S0002-9939-07-08935-6
PII: S 0002-9939(07)08935-6
Received by editor(s): May 23, 2006
Received by editor(s) in revised form: August 25, 2006, and September 19, 2006
Posted: 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
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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