Metric entropy of high dimensional distributions
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- by Ron Blei, Fuchang Gao and Wenbo V. Li PDF
- Proc. Amer. Math. Soc. 135 (2007), 4009-4018 Request permission
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.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
- MR Author ID: 290983
- Email: fuchang@uidaho.edu
- Wenbo V. Li
- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- Email: wli@math.udel.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2341952