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Original Articles

Computing maximum likelihood estimators of a log-concave density function

Pages 561-574 | Published online: 01 Aug 2007

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Guenther Walther, Alnur Ali, Xinyue Shen & Stephen Boyd. (2022) Confidence Bands for a Log-Concave Density. Journal of Computational and Graphical Statistics 31:4, pages 1426-1438.
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Samuel Müller & Kaspar Rufibach. (2009) Smooth tail-index estimation. Journal of Statistical Computation and Simulation 79:9, pages 1155-1167.
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Articles from other publishers (27)

Fadoua Balabdaoui & Harald Besdziek. (2024) Maximum likelihood estimation of the log-concave component in a semi-parametric mixture with a standard normal density. Journal of Statistical Planning and Inference 230, pages 106113.
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Mijeong Kim. (2023) Appropriate use of parametric and nonparametric methods in estimating regression models with various shapes of errors. Stat 12:1.
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Alexandros Grosdos, Alexander Heaton, Kaie Kubjas, Olga Kuznetsova, Georgy Scholten & Miruna-Ştefana Sorea. (2023) Exact solutions in log-concave maximum likelihood estimation. Advances in Applied Mathematics 143, pages 102448.
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Sunyul Kim & Byungtae Seo. (2020) Modal linear regression using log-concave distributions. Journal of the Korean Statistical Society 50:2, pages 479-494.
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Fadoua Balabdaoui & Yulia Kulagina. (2020) Completely monotone distributions: Mixing, approximation and estimation of number of species. Computational Statistics & Data Analysis 150, pages 107014.
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Sijia Xiang, Weixin Yao & Guangren Yang. (2019) An Overview of Semiparametric Extensions of Finite Mixture Models. Statistical Science 34:3.
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Robert Bassett & Julio Deride. (2018) Maximum a posteriori estimators as a limit of Bayes estimators. Mathematical Programming 174:1-2, pages 129-144.
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Yong Wang. (2018) Computation of the nonparametric maximum likelihood estimate of a univariate log‐concave density. WIREs Computational Statistics 11:1.
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Sunyul Kim & Byungtae Seo. (2018) Linear regression under log-concave and Gaussian scale mixture errors: comparative study. Communications for Statistical Applications and Methods 25:6, pages 633-645.
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Denis ChetverikovAndres SantosAzeem M. Shaikh. (2018) The Econometrics of Shape Restrictions. Annual Review of Economics 10:1, pages 31-63.
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Yu Liu & Yong Wang. (2018) A fast algorithm for univariate log‐concave density estimation. Australian & New Zealand Journal of Statistics 60:2, pages 258-275.
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Fadoua Balabdaoui & Charles R. Doss. (2018) Inference for a two-component mixture of symmetric distributions under log-concavity. Bernoulli 24:2.
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Hao Hu, Weixin Yao & Yichao Wu. (2017) The robust EM-type algorithms for log-concave mixtures of regression models. Computational Statistics & Data Analysis 111, pages 14-26.
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Hao Hu, Yichao Wu & Weixin Yao. (2016) Maximum likelihood estimation of the mixture of log-concave densities. Computational Statistics & Data Analysis 101, pages 137-147.
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Clifford Anderson-Bergman & Yaming Yu. (2015) Computing the log concave NPMLE for interval censored data. Statistics and Computing 26:4, pages 813-826.
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Johannes O. Royset & Roger J-B Wets. (2015) Fusion of hard and soft information in nonparametric density estimation. European Journal of Operational Research 247:2, pages 532-547.
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David Lucy & Grzegorz Zadora. (2011) Mixed effects modelling for glass category estimation from glass refractive indices. Forensic Science International.
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Arseni Seregin & Jon A. Wellner. (2010) Nonparametric estimation of multivariate convex-transformed densities. The Annals of Statistics 38:6.
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Madeleine Cule, Richard Samworth & Michael Stewart. (2010) Maximum Likelihood Estimation of a Multi-Dimensional Log-Concave Density. Journal of the Royal Statistical Society Series B: Statistical Methodology 72:5, pages 545-607.
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Roger Koenker & Ivan Mizera. (2010) Quasi-concave density estimation. The Annals of Statistics 38:5.
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Kaspar Rufibach. (2010) An active set algorithm to estimate parameters in generalized linear models with ordered predictors. Computational Statistics & Data Analysis 54:6, pages 1442-1456.
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Darinka Dentcheva & Spiridon Penev. (2010) Shape-restricted inference for Lorenz curves using duality theory. Statistics & Probability Letters 80:5-6, pages 403-412.
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Madeleine Cule & Richard Samworth. (2010) Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density. Electronic Journal of Statistics 4:none.
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Guenther Walther. (2009) Inference and Modeling with Log-concave Distributions. Statistical Science 24:3.
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Fadoua Balabdaoui, Kaspar Rufibach & Jon A. Wellner. (2009) Limit distribution theory for maximum likelihood estimation of a log-concave density. The Annals of Statistics 37:3.
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Lutz Dümbgen & Kaspar Rufibach. (2009) Maximum likelihood estimation of a log-concave density and its distribution function: Basic properties and uniform consistency. Bernoulli 15:1.
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George T. Chang & Guenther Walther. (2007) Clustering with mixtures of log-concave distributions. Computational Statistics & Data Analysis 51:12, pages 6242-6251.
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