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

@article{Huang2022ConsistentSD,
title={Consistent second-order discrete kernel smoothing using dispersed Conway-Maxwell-Poisson kernels},
author={Alan Huang and Lucas Sippel and Thomas Fung},
journal={Comput. Stat.},
year={2022},
volume={37},
pages={551-563}
}
• Published 7 October 2020
• Computer Science
• Comput. Stat.
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…
Asymptotic properties of the normalized discrete associated-kernel estimator for probability mass function
• Mathematics, Computer Science
• 2022
This paper shows, under some regularity and non-restrictive assumptions on the associated-kernel, that the normalizing random variable converges in mean square to 1 and derives the consistency and the asymptotic normality of the proposed estimator.
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 17 REFERENCES
Discrete associated kernels method and extensions
• Mathematics, Computer Science
• 2011
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
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
On finite sample properties of nonparametric discrete asymmetric kernel estimators
This study investigates the class of discrete asymmetric kernels and their resulting non-consistent estimators, but this theoretical drawback of the estimators is balanced by some interesting features in small/medium samples.
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
Discrete Poisson kernel density estimation-with an application to wildcat coal strikes
• Mathematics, Computer Science
• 1999
A nonparametric Poisson kernel density estimation technique for discrete distributions is proposed and applied to approximate the distribution of coal mine wildcat strikes in the United States.
Kernel density estimation via diffusion
• Computer Science
• 2010
A new adaptive kernel density estimator based on linear diffusion processes that builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate and a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods.
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.
• Mathematics
• 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.