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Resampling-based confidence regions and multiple tests for a correlated random vector. (English) Zbl 1203.62030

Bshouty, Nader H. (ed.) et al., Learning theory. 20th annual conference on learning theory, COLT 2007, San Diego, CA, USA, June 13–15, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72925-9). Lecture Notes in Computer Science 4539. Lecture Notes in Artificial Intelligence, 127-141 (2007).
Summary: We study generalized bootstrapped confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure, with a non-asymptotic control of the confidence level. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution. We consider two approaches, the first based on a concentration principle and the second on a direct boostrapped quantile. The first one allows us to deal with a very large class of resampling weights while our results for the second are restricted to Rademacher weights. However, the second method seems more accurate in practice. Our results are motivated by multiple testing problems, and we show on simulations that our procedures are better than the Bonferroni procedure (union bound) as soon as the observed vector has sufficiently correlated coordinates.
For the entire collection see [Zbl 1121.68002].

MSC:

62F40 Bootstrap, jackknife and other resampling methods
62F25 Parametric tolerance and confidence regions
62H15 Hypothesis testing in multivariate analysis
62J15 Paired and multiple comparisons; multiple testing
65C60 Computational problems in statistics (MSC2010)
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