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Assessing log-concavity of multivariate densities

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  • Hazelton, Martin L.

Abstract

We develop a test for log-concavity of multivariate densities. The method uses kernel density estimation, where the test statistic is the smallest bandwidth for which the estimate is log-concave. We examine the properties of this technique through numerical studies.

Suggested Citation

  • Hazelton, Martin L., 2011. "Assessing log-concavity of multivariate densities," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 121-125, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:121-125
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    References listed on IDEAS

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    1. Walther G., 2002. "Detecting the Presence of Mixing with Multiscale Maximum Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 508-513, June.
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    4. Eilers, Paul H.C. & Borgdorff, M.W., 2007. "Non-parametric log-concave mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5444-5451, July.
    5. Chang, George T. & Walther, Guenther, 2007. "Clustering with mixtures of log-concave distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6242-6251, August.
    6. Hazelton, Martin L. & Marshall, Jonathan C., 2009. "Linear boundary kernels for bivariate density estimation," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 999-1003, April.
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    Cited by:

    1. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.
    2. Fadoua Balabdaoui & Hanna Jankowski & Kaspar Rufibach & Marios Pavlides, 2013. "Asymptotics of the discrete log-concave maximum likelihood estimator and related applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 769-790, September.
    3. 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.

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