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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.
Published electronically:
September 7, 2007
MathSciNet review:
2341952
Full-text PDF Free Access
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Abstract: Let  be the collection of all  -dimensional probability distribution functions on ![$ [0,1]^d$](/proc/2007-135-12/S0002-9939-07-08935-6/gif-abstract0/img3.gif) ,  . The metric entropy of  under the ![$ L_2([0,1]^d)$](/proc/2007-135-12/S0002-9939-07-08935-6/gif-abstract0/img6.gif) 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.
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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:
http://dx.doi.org/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
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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