Consistent second-order discrete kernel smoothing using dispersed Conway–Maxwell–Poisson kernels

Alan Huang*, Lucas Sippel, Thomas Fung

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero probability estimation both within the observed range of counts and outside into the tails of the distribution. To circumvent this, we formulate a novel second-order discrete kernel smoother based on the recently developed mean-parametrized Conway–Maxwell–Poisson distribution which allows for both over- and under-dispersion. Two automated bandwidth selection approaches, one based on a simple minimization of the Kullback–Leibler divergence and another based on a more computationally demanding cross-validation criterion, are introduced. Both methods exhibit excellent small and large sample performance. Computational results on simulated datasets from a range of target distributions illustrate the flexibility and accuracy of the proposed method compared to existing smoothed and unsmoothed estimators. The method is applied to the modelling of somite counts in earthworms, and the number of development days of insect pests on the Hura tree.

    Original languageEnglish
    Pages (from-to)551-563
    Number of pages13
    JournalComputational Statistics
    Issue number2
    Early online date23 Aug 2021
    Publication statusPublished - Apr 2022


    • Mean-parametrized Conway-Maxwell-Poisson distribution
    • Discrete associated kernel smoothing
    • Histogram smoothing
    • Minimum Kullback-Leibler divergence
    • Cross-validated bandwidth


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