Álvarez-Esteban, Pedro César; del Barrio, Eustasio; Cuesta-Albertos, Juan Antonio; Matrán, Carlos Trimmed comparison of distributions. (English) Zbl 1471.62262 J. Am. Stat. Assoc. 103, No. 482, 697-704 (2008). Summary: 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. Cited in 17 Documents MSC: 62E20 Asymptotic distribution theory in statistics Keywords:asymptotics; impartial trimming; similarity; trimmed distributions; Wasserstein distance PDFBibTeX XMLCite \textit{P. C. Álvarez-Esteban} et al., J. Am. Stat. Assoc. 103, No. 482, 697--704 (2008; Zbl 1471.62262) Full Text: DOI