# On finite sample properties of nonparametric discrete asymmetric kernel estimators

## TL;DR

This paper analyzes the finite sample properties of nonparametric discrete asymmetric kernel estimators, highlighting their small-sample advantages and comparing kernel performances through simulations and real data applications.

## Contribution

It investigates the properties of discrete asymmetric kernels, especially their small-sample performance, and identifies conditions under which the binomial kernel outperforms others.

## Key findings

- Binomial kernel outperforms other asymmetric kernels in small samples.
- Discrete asymmetric kernels have non-consistent estimators but useful small-sample features.
- Simulation and real data analyses demonstrate kernel performance differences.

## 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 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. The role of modal probability and variance of discrete asymmetric kernels is highlighted to help better understand the performance of these kernels, in particular how the binomial kernel outperforms other asymmetric kernels. The performance of discrete asymmetric kernel estimators of probability mass functions is illustrated using simulations, in addition to applications to real data sets.