Multivariate log-concave distributions as a nearly parametric model

DOI10.1524/stnd.2011.1073zbMath1245.62060arXiv0907.0250OpenAlexW2951806534MaRDI QIDQ3104435

Lutz Dümbgen, Dominic Schuhmacher, André Hüsler

Publication date: 19 December 2011

Published in: Statistics & Risk Modeling (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0250

zbMATH Keywords

momentstotal variationLaplace transformsweak continuityconfidence setslog-concavity

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Characterization and structure theory for multivariate probability distributions; copulas (62H05)

Related Items

Global rates of convergence of the MLEs of log-concave and \(s\)-concave densities ⋮ On the Bartlett correction of empirical likelihood for Gaussian long-memory time series ⋮ Nonparametric least squares estimation of a multivariate convex regression function ⋮ Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density ⋮ Recent progress in log-concave density estimation ⋮ Local continuity of log-concave projection, with applications to estimation under model misspecification ⋮ Bi-log-concave distribution functions ⋮ Maximum-likelihood estimation of a log-concave density based on censored data ⋮ Approximation by log-concave distributions, with applications to regression ⋮ Semiparametric Time Series Models with Log‐concave Innovations: Maximum Likelihood Estimation and its Consistency

Uses Software

• LogConcDEAD

Cites Work

• Maximum likelihood estimation of a log-concave density and its distribution function: basic properties and uniform consistency
• The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
• Inference and modeling with log-concave distributions
• A note on the measurability of convex sets
• One-sided inference about functionals of a density
• Logconcavity versus logconvexity: A complete characterization
• Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
• Consistency of multivariate log-concave density estimators
• Log-concave probability and its applications
• The Nonexistence of Certain Statistical Procedures in Nonparametric Problems