We consider robust estimation of wrapped models to multivariate circular data that are points on the surface of a $p$-torus based on the weighted likelihood methodology.Robust model fitting is achieved by a set of weighted likelihood estimating equations, based on the computation of data dependent weights aimed to down-weight anomalous values, such as unexpected directions that do not share the main pattern of the bulk of the data. Weighted likelihood estimating equations with weights evaluated on the torus orobtained after unwrapping the data onto the Euclidean space are proposed and compared. Asymptotic properties and robustness features of the estimators under study have been studied, whereas their finite sample behavior has been investigated by Monte Carlo numerical experiment and real data examples.

翻译：本文考虑基于加权似然方法对多元圆形数据（即分布在 $p$-环面上的点）的包裹模型进行稳健估计。通过一组加权似然估计方程实现稳健模型拟合，该方程基于数据依赖权重的计算，旨在降低异常值（例如未遵循数据主体主要模式的意外方向）的权重。本文提出并比较了在环面上计算权重或通过将数据解包到欧几里得空间后获得权重的加权似然估计方程。研究分析了所估计量的渐近性质和稳健性特征，并通过蒙特卡洛数值实验和真实数据示例探究了其在有限样本下的表现。