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.

翻译：异常环形观测值在环面上的出现会严重影响多元冯·米塞斯分布的参数估计。本文通过加权似然方法解决了多元冯·米塞斯模型的稳健拟合问题。其核心要素包括多元环形数据的非参数密度估计以及适当加权估计方程的定义。文中讨论了一些理论性质。通过蒙特卡洛数值研究和实证应用，对所提出的加权似然估计量在有限样本下的表现进行了考察。