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LogConcDEAD: An R Package for Maximum Likelihood Estimation of a Multivariate Log-Concave Density

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  • Cule, Madeleine
  • Gramacy, Robert B.
  • Samworth, Richard

Abstract

In this article we introduce the R package LogConcDEAD (Log-concave density estimation in arbitrary dimensions). Its main function is to compute the nonparametric maximum likelihood estimator of a log-concave density. Functions for plotting, sampling from the density estimate and evaluating the density estimate are provided. All of the functions available in the package are illustrated using simple, reproducible examples with simulated data.

Suggested Citation

  • Cule, Madeleine & Gramacy, Robert B. & Samworth, Richard, 2009. "LogConcDEAD: An R Package for Maximum Likelihood Estimation of a Multivariate Log-Concave Density," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i02).
    • Handle: RePEc:jss:jstsof:v:029:i02
    DOI: http://hdl.handle.net/10.18637/jss.v029.i02
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    References listed on IDEAS

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    1. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
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    Cited by:

    1. S. O. Tickle & I. A. Eckley & P. Fearnhead, 2021. "A computationally efficient, high‐dimensional multiple changepoint procedure with application to global terrorism incidence," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1303-1325, October.
    2. Elina Robeva & Bernd Sturmfels & Ngoc Tran & Caroline Uhler, 2021. "Maximum likelihood estimation for totally positive log‐concave densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 817-844, September.
    3. Egger, Peter Hannes & Egger, Peter, 2016. "Heterogeneous Effects of Tariff and Nontariff Policy Barriers in General Equilibrium," VfS Annual Conference 2016 (Augsburg): Demographic Change 145675, Verein für Socialpolitik / German Economic Association.
    4. 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, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    5. Chun Yu & Weixin Yao & Guangren Yang, 2020. "A Selective Overview and Comparison of Robust Mixture Regression Estimators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 176-202, April.
    6. repec:jss:jstsof:39:i06 is not listed on IDEAS
    7. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    8. Rufibach Kaspar, 2012. "A Smooth ROC Curve Estimator Based on Log-Concave Density Estimates," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-29, April.
    9. Hu, Hao & Wu, Yichao & Yao, Weixin, 2016. "Maximum likelihood estimation of the mixture of log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 137-147.
    10. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2021. "Shape Constrained Kernel PDF and PMF Estimation," Department of Economics Working Papers 2021-05, McMaster University.
    11. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2023. "Randomized geometric tools for anomaly detection in stock markets," Post-Print hal-04223511, HAL.
    12. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2022. "Randomized geometric tools for anomaly detection in stock markets," Papers 2205.03852, arXiv.org, revised May 2022.
    13. Schuhmacher Dominic & Hüsler André & Dümbgen Lutz, 2011. "Multivariate log-concave distributions as a nearly parametric model," Statistics & Risk Modeling, De Gruyter, vol. 28(3), pages 277-295, September.

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