Metric entropy of high dimensional distributions

Blei, Ron; Gao, Fuchang; Li, Wenbo

doi:10.1090/S0002-9939-07-08935-6

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.

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