# 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} }

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…

## 2 Citations

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

- Mathematics
- 2020

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…

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