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Bandwidth selection for kernel log-density estimation

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  • Hazelton, Martin L.
  • Cox, Murray P.

Abstract

Kernel estimation of the logarithm of a probability density function at a given evaluation point is studied. The properties of the kernel log-density estimator are heavily influenced by the unboundedness of the log function at zero. In particular, standard asymptotic expansions can provide a poor guide to finite sample behaviour for this estimator, with consequences for the choice of methodology for bandwidth selection. In response, a new approximate cross-validation bandwidth selector is developed. Its theoretical properties are explored and its finite sample behaviour examined in numerical experiments. The proposed methodology is then applied to estimation of log-likelihoods for a complex genetic model used in determining migration rates between village communities on the Indonesian island of Sumba.

Suggested Citation

  • Hazelton, Martin L. & Cox, Murray P., 2016. "Bandwidth selection for kernel log-density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 56-67.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:56-67
    DOI: 10.1016/j.csda.2016.05.003
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    References listed on IDEAS

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    1. Mikael Sunnåker & Alberto Giovanni Busetto & Elina Numminen & Jukka Corander & Matthieu Foll & Christophe Dessimoz, 2013. "Approximate Bayesian Computation," PLOS Computational Biology, Public Library of Science, vol. 9(1), pages 1-10, January.
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    4. Tarn Duong & Martin L. Hazelton, 2005. "Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 485-506, September.
    5. repec:dau:papers:123456789/5724 is not listed on IDEAS
    6. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
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