Resampling-based confidence regions and multiple tests for a correlated random vector - Archive ouverte HAL Access content directly
Book Sections Year : 2007

Resampling-based confidence regions and multiple tests for a correlated random vector

(1, 2) , (3) , (4)
1
2
3
4

Abstract

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.
Fichier principal
Vignette du fichier
ABR07court.pdf (215.52 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00125670 , version 1 (22-01-2007)

Identifiers

Cite

Sylvain Arlot, Gilles Blanchard, Etienne Roquain. Resampling-based confidence regions and multiple tests for a correlated random vector. Nader H. Bshouty and Claudio Gentile. Learning Theory 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, USA; June 13-15, 2007. Proceedings, Springer Berlin / Heidelberg, pp.127-141, 2007, Lecture Notes in Computer Science - Volume 4539/2007, ⟨10.1007/978-3-540-72927-3_11⟩. ⟨hal-00125670⟩
403 View
115 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More