Maximum likelihood estimation of a log-concave density and its distribution function: basic properties and uniform consistency
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Publication:605846
DOI10.3150/08-BEJ141zbMath1200.62030arXiv0709.0334WikidataQ61810959 ScholiaQ61810959MaRDI QIDQ605846
Publication date: 15 November 2010
Published in: Bernoulli (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0709.0334
exponential inequalityadaptivityhazard functionshape constraintsgap problembracketingmethod of caricatures
Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Estimation in survival analysis and censored data (62N02)
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Cites Work
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- Unnamed Item
- Clustering with mixtures of log-concave distributions
- Maximum likelihood estimation of a log-concave density and its distribution function: basic properties and uniform consistency
- Consistency of concave regression with an application to current-status data
- Uniform central limit theorems for kernel density estimators
- An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation
- Limit distribution theory for maximum likelihood estimation of a log-concave density
- The oscillation behavior of empirical processes
- On the estimation of a probability density function by the maximum penalized likelihood method
- MCMC convergence diagnosis via multivariate bounds on log-concave densities
- New goodness-of-fit tests and their application to nonparametric confidence sets
- Density estimation by wavelet thresholding
- Maximum likelihood estimation of smooth monotone and unimodal densities.
- Estimation of a convex function: Characterizations and asymptotic theory.
- Estimation of a \(k\)-monotone density: limit distribution theory and the spline connection
- Log-concave probability and its applications
- The behavior of the NPMLE of a decreasing density near the boundaries of the support
- Testing for monotone increasing hazard rate
- Smooth tail-index estimation
- A Lower Bound on the Risks of Non-Parametric Estimates of Densities in the Uniform Metric
- Asymptotically minimax estimation of concave and convex distribution functions
- Detecting the Presence of Mixing with Multiscale Maximum Likelihood
- Estimating the Derivative of a Convex Density
- Consistent maximum likelihood estimation of a unimodal density using shape restrictions
- A Kiefer-Wolfowitz theorem for convex densities
- Marshall’s lemma for convex density estimation
- The Support Reduction Algorithm for Computing Non‐Parametric Function Estimates in Mixture Models
- Computing maximum likelihood estimators of a log-concave density function
- Maximum Likelihood Estimation of a Unimodal Density Function
- A semi-parametric model for censored and passively registered data