Inference for empirical Wasserstein distances on finite spaces

• 成果类型: Article
• 署名作者: Sommerfeld, Max; Munk, Axel
• 署名单位: University of Gottingen; Max Planck Society
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12236
• 发表日期: 2018
• 页码: 219-238
• 关键词: DISTRIBUTIONS; CONVERGENCE; barycenters; validation; MODEL

摘要

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic distribution of empirical Wasserstein distances as the optimal value of a linear programme with random objective function. This facilitates statistical inference (e.g. confidence intervals for sample-based Wasserstein distances) in large generality. Our proof is based on directional Hadamard differentiability. Failure of the classical bootstrap and alternatives are discussed. The utility of the distributional results is illustrated on two data sets.