Wasserstein projection estimators for circular distributions

TL;DR

This paper introduces Wasserstein projection estimators for circular distributions, demonstrating their accuracy and robustness compared to traditional methods through numerical experiments.

Contribution

It develops algorithms for Wasserstein projection estimators on circles and compares their performance to maximum likelihood estimators.

Findings

Wasserstein projection estimators have accuracy comparable to MLE.

The $L^1$-Wasserstein estimator is robust against noise.

Algorithms are provided for computing these estimators on circular data.

Abstract

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.