Entropy estimate for high-dimensional monotonic functions

We establish upper and lower bounds for the metric entropy and bracketing entropy of the class of d-dimensional bounded monotonic functions under Lp 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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Year of publication:	2007
Authors:	Gao, Fuchang ; Wellner, Jon A.
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 98.2007, 9, p. 1751-1764
Publisher:	Elsevier
Keywords:	Block decreasing density Metric entropy Bracketing entropy Maximum likelihood estimator

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005153112