University of Cambridge > > Probability > Talagrand's concentration inequality for empirical processes

Talagrand's concentration inequality for empirical processes

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Berestycki.

This is an expository talk about a deep probability inequality due to Talagrand (Invent. Math. 1996, cf. Ledoux’s book in 2001), which gives a Prohorov- (and then also Bernstein-) type exponential bound for the concentration of the supremum of an empirical process around its mean. I will try to discuss the following points: A) Some ideas of the proof, in particular the proof due to Ledoux using logarithmic Sobolev inequalities, which is related to the more general “concentration of measure” phenomenon. B) Discuss a variety of probabilistic applications, which should show how versatile this inequality is, in particular that it reproduces most known exp. inequalities for i.i.d. sums of (possibly Banach-)valued random variables. C) Discuss recent statistical applications to adaptive estimation, model selection problems, Rademacher processes, and almost sure limit laws (LIL-type results).

This talk is part of the Probability series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity