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

Author

Listed:
  • Alan Huang

    (University of Queensland)

  • Lucas Sippel

    (University of Queensland)

  • Thomas Fung

    (Macquarie University)

Abstract

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.

Suggested Citation

  • Alan Huang & Lucas Sippel & Thomas Fung, 2022. "Consistent second-order discrete kernel smoothing using dispersed Conway–Maxwell–Poisson kernels," Computational Statistics, Springer, vol. 37(2), pages 551-563, April.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:2:d:10.1007_s00180-021-01144-w
    DOI: 10.1007/s00180-021-01144-w
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    References listed on IDEAS

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    1. Lawrence Marsh & Kajal Mukhopadhyay, 1999. "Discrete Poisson kernel density estimation-with an application to wildcat coal strikes," Applied Economics Letters, Taylor & Francis Journals, vol. 6(6), pages 393-396.
    2. Kokonendji, Célestin C. & Zocchi, Silvio S., 2010. "Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1655-1662, November.
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    Cited by:

    1. Doho, Libaud Rudy Aurelien & Somé, Sobom Matthieu & Banto, Jean Michel, 2023. "Inflation and west African sectoral stock price indices: An asymmetric kernel method analysis," Emerging Markets Review, Elsevier, vol. 54(C).
    2. Senga Kiessé, Tristan & Durrieu, Gilles, 2024. "On a discrete symmetric optimal associated kernel for estimating count data distributions," Statistics & Probability Letters, Elsevier, vol. 208(C).
    3. Sobom M. Somé & Célestin C. Kokonendji & Nawel Belaid & Smail Adjabi & Rahma Abid, 2023. "Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 843-865, September.

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