Entropy estimate for high-dimensional monotonic functions

Authors:
Fuchang Gao;Jon A. Wellner
Affiliations:
Department of Mathematics, University of Idaho, P.O. Box 441103, Moscow, ID 83844-1103, USA;Department of Statistics, University of Washington, P.O. Box 354322. Seattle, WA 98195-4322, USA
Venue:
Journal of Multivariate Analysis
Year:
2007

Citing 3
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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 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.