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). 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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Volume (Year): 98 (2007)
Issue (Month): 9 (October)
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- Polonik, W., 1995. "Density Estimation under Qualitative Assumptions in Higher Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 55(1), pages 61-81, October.
- Biau, Gérard & Devroye, Luc, 2003. "On the risk of estimates for block decreasing densities," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 143-165, July.
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