Wasserstein projection estimators for circular distributions

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 Wasserstein projection estimators attain estimation accuracy comparable to the maximum likelihood estimator. In addition, the Wasserstein projection estimators are found to be robust against noise contamination.