稳健的圆数据分散度度量及其异常检测规则
Robust measures of dispersion for circular data with an anomaly detection rule
AI总结：
本文提出稳健的圆数据分散度度量方法，并开发异常检测程序以识别圆数据中的异常值。
摘要：
表示方向或周期性观测的圆变量出现在许多领域，如生物学和环境科学。处理圆数据时一个重要问题是如何稳健地估计其分散度，避免异常值的过度影响。本文将三种稳健的分散度度量从直线扩展到圆。通过影响函数和相对偏倚曲线研究其稳健性。从这些分散度度量中可以推导出圆分布参数的稳健估计器。这导致了von Mises分布集中参数和包裹正态分布分散参数的稳健估计器。获得了它们的崩溃值和统计效率，并在模拟研究中进行了比较。基于表现最佳的估计器，开发了一种稳健的圆异常检测程序，并通过圆形小提琴图可视化异常值。分析了三个真实数据集。
英文摘要：
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.
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