Entropy estimate for high-dimensional monotonic functions

DOI10.1016/j.jmva.2006.09.003zbMath1221.62008arXivmath/0512641OpenAlexW2127991572MaRDI QIDQ2474241

Jon A. Wellner, Fuchang Gao

Publication date: 5 March 2008

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512641

zbMATH Keywords

maximum likelihood estimatormetric entropybracketing entropyblock decreasing density

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Statistical aspects of information-theoretic topics (62B10)

Related Items

Optimal classification and nonparametric regression for functional data, Bracketing numbers of convex and \(m\)-monotone functions on polytopes, The limiting behavior of isotonic and convex regression estimators when the model is misspecified, Minimax estimation of the mode of functional data, Local asymptotic minimax theory for block-decreasing densities, Adaptive risk bounds in unimodal regression, The difficulty of Monte Carlo approximation of multivariate monotone functions, Sharp oracle inequalities for least squares estimators in shape restricted regression, Towards optimal estimation of bivariate isotonic matrices with unknown permutations, High-dimensional nonparametric density estimation via symmetry and shape constraints, Semiparametric additive isotonic regression, Set structured global empirical risk minimizers are rate optimal in general dimensions, On the rate of convergence of the maximum likelihood estimator of a \(k\)-monotone density, Isotonic regression in general dimensions

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