Entropy Estimate For High Dimensional Monotonic Functions

Details Entropy Estimate For High Dimensional Monotonic Functions Entropy Estimate For High Dimensional Monotonic Functions

2005-12-29

arxiv.org/abs/math/0512641v1

Mathematics

Statistics Theory

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

Scientific paper

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 $pd/(d-1)$. 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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