Estimation of a multivariate von Mises distribution for contaminated torus data

TL;DR

This paper develops a robust method for estimating the multivariate von Mises distribution in contaminated torus data using weighted likelihood, addressing issues caused by atypical observations.

Contribution

It introduces a weighted likelihood approach with non-parametric density estimation for robust parameter fitting of multivariate von Mises models.

Findings

The proposed estimator shows improved robustness in simulations.

The method performs well in empirical applications.

Theoretical properties of the estimator are discussed.

Abstract

The occurrence of atypical circular observations on the torus can badly affect parameter estimation of the multivariate von Mises distribution. This paper addresses the problem of robust fitting of the multivariate von Mises model using the weighted likelihood methodology. The key ingredients are non-parametric density estimation for multivariate circular data and the definition of appropriate weighted estimating equations. Some theoretical properties are discussed. The finite sample behavior of the proposed weighted likelihood estimator has been investigated by Monte Carlo numerical studies and empirical applications.