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

@article{Huang2021ConsistentSD,
title={Consistent second-order discrete kernel smoothing using dispersed Conway–Maxwell–Poisson kernels},
author={Alan Huang and Lucas Sippel and Thomas Fung},
journal={Computational Statistics},
year={2021}
}
• Published 7 October 2020
• Mathematics
• Computational Statistics
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 overand under-dispersion. Two automated bandwidth selection approaches, one based…
1 Citations

## Figures and Tables from this paper

On arbitrarily underdispersed Conway-Maxwell-Poisson distributions
We show that the Conway--Maxwell--Poisson distribution can be arbitrarily underdispersed when parametrized via its mean. More precisely, if the mean $\mu$ is an integer then the limiting distribution

## References

SHOWING 1-10 OF 20 REFERENCES
Discrete associated kernels method and extensions
• Mathematics
• 2011
Abstract Discrete kernel estimation of a probability mass function (p.m.f.), often mentioned in the literature, has been far less investigated in comparison with continuous kernel estimation of a
Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts
Conway–Maxwell–Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in
Discrete triangular distributions and non-parametric estimation for probability mass function
• Mathematics
• 2007
Abstract Discrete triangular distributions are introduced, in order to serve as kernels in the non-parametric estimation for probability mass function. They are locally symmetric around every point
On finite sample properties of nonparametric discrete asymmetric kernel estimators
ABSTRACT The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the
On finite sample properties of nonparametric discrete asymmetric kernel estimators
ABSTRACTThe discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the
Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions
• Mathematics
• 2010
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
Discrete Poisson kernel density estimation-with an application to wildcat coal strikes
• Mathematics
• 1999
This paper proposes a nonparametric Poisson kernel density estimation technique for discrete distributions. Economists have been using continuous kernels to approximate discrete distributions. This
Kernel density estimation via diffusion
• Mathematics
• 2010
We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a
Remarks on Some Nonparametric Estimates of a Density Function
1. Summary. This note discusses some aspects of the estimation of the density function of a univariate probability distribution. All estimates of the density function satisfying relatively mild
Density Estimation for Statistics and Data Analysis.
• Computer Science
• 1988
The two main aims of the book are to explain how to estimate a density from a given data set and to explore how density estimates can be used, both in their own right and as an ingredient of other statistical procedures.