Computing confidence intervals for log-concave densities

DOI10.1016/j.csda.2014.01.020zbMath1506.62016OpenAlexW2100649339MaRDI QIDQ1623498

Mahdis Azadbakhsh, Xin Gao, Hanna K. Jankowski

Publication date: 23 November 2018

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.csda.2014.01.020

zbMATH Keywords

maximum likelihoodconfidence intervalnonparametric density estimationlog-concave

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Density estimation (62G07) Nonparametric tolerance and confidence regions (62G15)

Related Items

Confidence Bands for a Log-Concave Density ⋮ A law of the iterated logarithm for Grenander's estimator ⋮ Some developments in the theory of shape constrained inference ⋮ Circumventing superefficiency: an effective strategy for distributed computing in non-standard problems ⋮ A review of uncertainty quantification for density estimation ⋮ Univariate log-concave density estimation with symmetry or modal constraints

Uses Software

• ks
• logcondens
• cobs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Inference and modeling with log-concave distributions
• Inconsistency of bootstrap: the Grenander estimator
• Limit distribution theory for maximum likelihood estimation of a log-concave density
• A simple root \(n\) bandwidth selector
• Smoothing techniques. With implementation in S
• Subsampling
• A canonical process for estimation of convex functions: the ``invelope of integrated Brownian motion \(+t^ 4\).
• Estimation of a convex function: Characterizations and asymptotic theory.
• Likelihood ratio tests for monotone functions.
• Nonparametric and semiparametric models.
• Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
• Multivariate plug-in bandwidth selection
• Estimation of the mode
• Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen
• Detecting the Presence of Mixing with Multiscale Maximum Likelihood
• Maximum Likelihood Estimation of a Multi-Dimensional Log-Concave Density
• The Support Reduction Algorithm for Computing Non‐Parametric Function Estimates in Mixture Models
• Confidence Intervals for Current Status Data
• On the bootstrap in cube root asymptotics
• All of Nonparametric Statistics