Entropy estimate for \(k\)-monotone functions via small ball probability of integrated Brownian motions

DOI10.1214/ECP.v13-1357zbMath1194.60027OpenAlexW2129661466MaRDI QIDQ1038863

Fuchang Gao

Publication date: 20 November 2009

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/229922

zbMATH Keywords

\(k\)-monotone functionmetric entropysmall ball probability\(k\)-times integrated Brownian motion

Mathematics Subject Classification ID

Density estimation (62G07) Gaussian processes (60G15) Brownian motion (60J65) Applications of functional analysis in probability theory and statistics (46N30)

Related Items (6)

Bracketing numbers of convex and \(m\)-monotone functions on polytopes ⋮ Entropy of convex functions on \(\mathbb R^d\) ⋮ Small ball probabilities, metric entropy and Gaussian rough paths ⋮ A two stage \(k\)-monotone B-spline regression estimator: uniform Lipschitz property and optimal convergence rate ⋮ How many Laplace transforms of probability measures are there? ⋮ On the rate of convergence of the maximum likelihood estimator of a \(k\)-monotone density

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