Entropy Estimate For High Dimensional Monotonic Functions

Fuchang Gao; Jon A. Wellner

Entropy Estimate For High Dimensional Monotonic Functions

Statistics Theory 2007-06-13 v1 Classical Analysis and ODEs Statistics Theory

Authors: Fuchang Gao , Jon A. Wellner

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.

Keywords

topological entropy monotone functions mean dimension

Cite

@article{arxiv.math/0512641,
  title  = {Entropy Estimate For High Dimensional Monotonic Functions},
  author = {Fuchang Gao and Jon A. Wellner},
  journal= {arXiv preprint arXiv:math/0512641},
  year   = {2007}
}

Comments

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

Entropy Estimate For High Dimensional Monotonic Functions

Abstract

Keywords

Cite

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