Estimating the concentration parameter of a von Mises distribution: a systematic simulation benchmark

TL;DR

This paper systematically evaluates 12 estimators for the concentration parameter of the von Mises distribution across various dataset sizes and concentration levels, providing comprehensive benchmarks and insights into their performance.

Contribution

It offers a thorough simulation-based benchmark of 12 estimators for the von Mises concentration parameter, highlighting their behaviors across different data sizes and concentration values.

Findings

Estimators behave similarly for large datasets ($N \\geq 16$)

Estimators show more variability with small datasets

Performance metrics vary depending on the value of \\kappa$

Abstract

In directional statistics, the von Mises distribution is a key element in the analysis of circular data. While there is a general agreement regarding the estimation of its location parameter $\mu$, several methods have been proposed to estimate the concentration parameter $\kappa$. We here provide a thorough evaluation of the behavior of 12 such estimators for datasets of size $N$ ranging from 2 to 8\,192 generated with a $\kappa$ ranging from 0 to 100. We provide detailed results as well as a global analysis of the results, showing that (1) for a given $\kappa$, most estimators have behaviors that are very similar for large datasets ($N \geq 16$) and more variable for small datasets, and (2) for a given estimator, results are very similar if we consider the mean absolute error for $\kappa \leq 1$ and the mean relative absolute error for $\kappa \geq 1$.