Hypothesis Test and Confidence Analysis with Wasserstein Distance on General Dimension

Understand

We develop a general framework for statistical inference with the 1-Wasserstein distance.

• Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its excellent properties.
• However, hypothesis tests and a confidence analysis for the Wasserstein distance have not been established in a general multivariate setting.
• This is because the limit distribution of the empirical distribution with the Wasserstein distance is unavailable without strong restriction.