Approximation and estimation of \(s\)-concave densities via Rényi divergences

DOI10.1214/15-AOS1408zbMath1338.62105arXiv1505.00379WikidataQ42366123 ScholiaQ42366123MaRDI QIDQ292894

Qiyang Han, Jon A. Wellner

Publication date: 9 June 2016

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.00379

zbMATH Keywords

asymptotic distributionconsistencyprojectionmode estimationnonparametric estimation\(s\)-concavityshape constraints

Mathematics Subject Classification ID

Density estimation (62G07) Estimation in multivariate analysis (62H12) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items

Global rates of convergence of the MLEs of log-concave and \(s\)-concave densities, Approximation and estimation of \(s\)-concave densities via Rényi divergences, The Modal Age of Statistics, Inference for Local Parameters in Convexity Constrained Models, A Remark on the Grenander Estimator, Recent progress in log-concave density estimation, Shape constrained density estimation via penalized Rényi divergence, Local continuity of log-concave projection, with applications to estimation under model misspecification, Unnamed Item, Limit distribution theory for block estimators in multiple isotonic regression, High-dimensional nonparametric density estimation via symmetry and shape constraints, Oracle posterior contraction rates under hierarchical priors, A review of uncertainty quantification for density estimation, Confidence intervals for multiple isotonic regression and other monotone models, Set structured global empirical risk minimizers are rate optimal in general dimensions, Univariate log-concave density estimation with symmetry or modal constraints, Inference for the mode of a log-concave density

Uses Software

• Mosek
• LogConcDEAD
• logcondens

Cites Work

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