For statistical models on circles, we investigate performance of estimators defined as the projections of the empirical distribution with respect to the Wasserstein distance. We develop algorithms for computing the Wasserstein projection estimators based on a formula of the Wasserstein distances on circles. Numerical results on the von Mises, wrapped Cauchy, and sine-skewed von Mises distributions show that the accuracy of the Wasserstein projection estimators is comparable to the maximum likelihood estimator. In addition, the $L^1$-Wasserstein projection estimator is found to be robust against noise contamination.

翻译：针对圆环上的统计模型，我们研究了基于Wasserstein距离的经验分布投影所定义估计器的性能。基于圆环上Wasserstein距离的计算公式，我们开发了计算Wasserstein投影估计器的算法。在von Mises分布、缠绕柯西分布和正弦偏斜von Mises分布上的数值结果表明，Wasserstein投影估计器的精度与最大似然估计器相当。此外，研究发现$L^1$-Wasserstein投影估计器对噪声污染具有鲁棒性。