Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 103, Issue 482, Pages 697-704Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/016214508000000274
Keywords
asymptotics; impartial trimming; similarity; trimmed distributions; Wasserstein distance
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This article introduces an analysis of similarity of distributions based on the L-2-Wasserstein distance between trimmed distributions. Our main innovation is the use of the impartial trimming methodology, already considered in robust statistics, which we adapt to this setup. Instead of simply removing data at the tails to provide some robustness to the similarity analysis, we develop a data-driven trimming method aimed at maximizing similarity between distributions. Dissimilarity is then measured in terms of the distance between the optimally trimmed distributions. We provide illustrative examples showing the improvements over previous approaches and give the relevant asymptotic results to justify the use of this methodology in applications.
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