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Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Author

Listed:
  • Kokonendji, Célestin C.
  • Zocchi, Silvio S.

Abstract

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:21-22:p:1655-1662
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    Citations

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    Cited by:

    1. Kokonendji, Célestin C. & Varron, Davit, 2016. "Performance of discrete associated kernel estimators through the total variation distance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 225-235.
    2. T. Senga Kiessé & M. Rivoire, 2011. "Discrete semiparametric regression models with associated kernel and applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 927-941.
    3. Zougab, Nabil & Adjabi, Smail & Kokonendji, Célestin C., 2014. "Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 28-38.
    4. Shaul K. Bar-Lev & Gérard Letac, 2023. "A note on the discretization of natural exponential families on the real line," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 83-90, January.
    5. 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.
    6. Anna Gottard & Maria Iannario & Domenico Piccolo, 2016. "Varying uncertainty in CUB models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 225-244, June.
    7. Senga Kiessé, Tristan & Ventura, Anne, 2016. "Discrete non-parametric kernel estimation for global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 146(C), pages 47-54.

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