On Underdispersed Count Kernels for Smoothing Probability Mass Functions

Célestin C. Kokonendji (), Sobom M. Somé (), Youssef Esstafa and Marcelo Bourguignon
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Célestin C. Kokonendji: Laboratoire de Mathématiques de Besançon UMR 6623 CNRS-UBFC, Université Bourgogne Franche-Comté, 16 Route de Gray, CEDEX, 25030 Besançon, France
Sobom M. Somé: Laboratoire d’Analyse Numérique Informatique et de BIOmathématique, Université Joseph KI-ZERBO, Ouagadougou 03 BP 7021, Burkina Faso
Youssef Esstafa: Laboratoire Manceau de Mathématiques, Le Mans Université, Avenue Olivier Messiaen, CEDEX 09, 72085 Le Mans, France
Marcelo Bourguignon: Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078-970, Brazil

Stats, 2023, vol. 6, issue 4, 1-15

Abstract: Only a few count smoothers are available for the widespread use of discrete associated kernel estimators, and their constructions lack systematic approaches. This paper proposes the mean dispersion technique for building count kernels. It is only applicable to count distributions that exhibit the underdispersion property, which ensures the convergence of the corresponding estimators. In addition to the well-known binomial and recent CoM-Poisson kernels, we introduce two new ones such the double Poisson and gamma-count kernels. Despite the challenging problem of obtaining explicit expressions, these kernels effectively smooth densities. Their good performances are pointed out from both numerical and comparative analyses, particularly for small and moderate sample sizes. The optimal tuning parameter is here investigated by integrated squared errors. Also, the added advantage of faster computation times is really very interesting. Thus, the overall accuracy of two newly suggested kernels appears to be between the two old ones. Finally, an application including a tail probability estimation on a real count data and some concluding remarks are given.

Keywords: binomial kernel; CoM-Poisson kernel; double Poisson distribution; gamma-count distribution; integrated squared errors; mode dispersion; normalizing constant (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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