Entropy Estimate For High Dimensional Monotonic Functions

2005/12/29 by Fuchang Gao, Jon A. Wellner, Gao, Fuchang +1 · 1 citation
Mathematics · #41A46 #46E35 (primary) #62G05 #62G07 (secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Statistics Theory (math.ST) #math.CA #math.ST #msc:41A46 #msc:46E35 #msc:62G05 #msc:62G07 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0512641

11 pages. Submitted to Journal of Multivariate Analysis. See also http://www.stat.washington.edu/jaw/RESEARCH/PAPERS/available.html

arxiv created 2005/12/29 · arxiv updated 2009/12/01

Abstract

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under L^p norms. It is interesting to see that both the metric entropy and bracketing entropy have different behaviors for p<d/(d-1) and p>d/(d-1). We apply the new bounds for bracketing entropy to establish a global rate of convergence of the MLE of a d-dimensional monotone density.

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