Entropy estimate for high-dimensional monotonic functions

Fuchang Gao and Jon A. Wellner

Journal of Multivariate Analysis, 2007, vol. 98, issue 9, 1751-1764

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). 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: Block; decreasing; density; Metric; entropy; Bracketing; entropy; Maximum; likelihood; estimator (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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