Entropy estimate for high-dimensional monotonic functions |
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| Authors: | Fuchang Gao Jon A Wellner |
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| Institution: | a Department of Mathematics, University of Idaho, P.O. Box 441103, Moscow, ID 83844-1103, USA
b Department of Statistics, University of Washington, P.O. Box 354322. Seattle, WA 98195-4322, USA |
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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 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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| Keywords: | 41A25 62G05 |
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