Resampling-based confidence regions and multiple tests for a correlated random vector
Sylvain Arlot, Gilles Blanchard, Etienne Roquain
备注：
submitted to COLT
发表信息：
Learning Theory 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, USA; June 13-15, 2007. Proceedings, Springer Berlin / Heidelberg (Ed.) (2007) 127-141
We derive non-asymptotic confidence regions for the mean of a random vector whose coordinates have an unknown dependence structure. The random vector is supposed to be either Gaussian or to have a symmetric bounded distribution, and we observe $n$ i.i.d copies of it. The confidence regions are built using a data-dependent threshold based on a weighted bootstrap procedure. We consider two approaches, the first based on a concentration approach and the second on a direct boostrapped quantile approach. The first one allows 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.
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Faculty of Mathematics and Physics, Charles University（查理大学数学与物理学院）；Institute for Mathematical Stochastics, Otto-von-Guericke-Universität Magdeburg（马格德堡奥托·冯·古里克大学数学随机性研究所）；Department of Statistics, TU Dortmund University（多特蒙德工业大学统计系）
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