Journal
BERNOULLI
Volume 18, Issue 2, Pages 606-634Publisher
INT STATISTICAL INST
DOI: 10.3150/11-BEJ351
Keywords
asymptotics; bootstrap; consistency; mass transportation problem; over-fitting; robustness; similarity of distributions; trimmed probability; Wasserstein distance
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Funding
- Spanish Ministerio de Ciencia e Innovacion [MTM2008-06067-C02-01, 02]
- Consejeria de Educacion y Cultura de la Junta de Castilla y Leon [GR150]
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We say that two probabilities are similar at level a if they are contaminated versions (up to an a fraction) of the same common probability. We show how this model is related to minimal distances between sets of trimmed probabilities. Empirical versions turn out to present an overfitting effect in the sense that trimming beyond the similarity level results in trimmed samples that are closer than expected to each other. We show how this can be combined with a bootstrap approach to assess similarity from two data samples.
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