Circular variables that represent directions or periodic observations arise in many fields, such as biology and environmental sciences. An important issue when dealing with circular data is how to estimate their dispersion robustly, avoiding undue effects of anomalies. This work extends three robust dispersion measures from the line to the circle. Their robustness is studied via their influence functions and relative bias curves. From these dispersion measures, robust estimators of parameters of circular distributions can be derived. This yields robust estimators for the concentration parameter of the von Mises distribution and the dispersion parameter of the wrapped normal distribution. Their breakdown values and statistical efficiencies are obtained, and they are compared in a simulation study. Building on the best performing estimator, a robust circular anomaly detection procedure is developed, and employed to visualize outliers through a circular violin plot. Three real datasets are analyzed.

翻译：圆形变量表示方向或周期性观测值，广泛存在于生物学和环境科学等诸多领域。处理圆形数据时，一个关键问题是如何稳健地估计其离差，避免异常值造成不当影响。本研究将三种稳健离差度量从线性域推广至圆形域，通过影响函数与相对偏差曲线分析了其稳健性。基于这些离差度量，可推导出圆形分布参数的稳健估计量，由此得到冯·米塞斯分布集中参数与卷绕正态分布离差参数的稳健估计量。研究获得了这些估计量的崩溃值与统计效率，并通过模拟实验进行性能比较。基于表现最优的估计量，开发了稳健的圆形异常值检测流程，并采用圆形小提琴图实现异常值的可视化。本文最后对三个真实数据集进行了分析。