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Computation of the nonparametric maximum likelihood estimate of a univariate log‐concave density

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Algorithms for computing the nonparametric maximum likelihood estimate of a univariate log‐concave density are briefly described, and some relevant issues discussed. The fast few algorithms are further numerically compared in a small‐scale simulation study. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) Statistical and Graphical Methods of Data Analysis > Density Estimation Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Algorithms and Computational Methods > Algorithms
Density, log‐density and gradient functions of the nonparametric maximum likelihood estimators (NPMLEs) obtained from generic samples (n = 1,000) drawn from Exponential(1) and Normal(0, 1), respectively. Knots are indicated by small circles
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Algorithms and Computational Methods > Algorithms
Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Statistical and Graphical Methods of Data Analysis > Density Estimation
Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)

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