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SUMMARY:Gaussian Approximations and Bootstrap with p &gt\;&gt\; n. - Victo
 r Chernozhukov\, MIT
DTSTART:20140624T141500Z
DTEND:20140624T144500Z
UID:TALK53108@talks.cam.ac.uk
CONTACT:37296
DESCRIPTION:We show that central limit theorems hold for high-dimensional 
 normalized means hitting high dimensional rectangles (and\, more generally
 \, convex sets formed as sparse deformations of rectangles). These results
  apply even when p>> n. These theorems provide Gaussian distributional app
 roximations that are not pivotal\, but they can be consistently estimated 
 via Gaussian multiplier methods (Gine and Zinn) and the empirical bootstra
 p. These results generalize to the suprema of empirical processes indexed 
 by function sets with diverging complexity\, and are useful for building c
 onfidence bands in modern high-dimensional and nonparametric problems  (Gi
 ne and Nickl) and for multiple testing via the step-down methods. This is 
 joint work with Denis Chetverikov (UCLA) and Kengo Kato (Tokyo). Refs: arx
 iv 1212.6906\, 1212.6885\,1303.7152.
LOCATION:Centre for Mathematical Sciences\, Meeting Room 2
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