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

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

2007-01-22

arxiv.org/abs/math/0701605v1

Learning Theory 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, USA; June 13-15, 2007. Proceedings, Sprin

Mathematics

Statistics Theory

submitted to COLT

Scientific paper

10.1007/978-3-540-72927-3_11

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.

Affiliated with

Also associated with

No associations

Rating

Resampling-based confidence regions and multiple tests for a correlated random vector does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Resampling-based confidence regions and multiple tests for a correlated random vector, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Resampling-based confidence regions and multiple tests for a correlated random vector will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-516682