Concentration inequalities for smooth random fields

2013/07/05 by Denis Belomestny, Belomestny, Denis, Vladimir Spokoiny +1
Mathematics · #62F25 #62H12 #62J12 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62F25 #msc:62H12 #msc:62J12 #stat.TH

paper · pdf · doi:10.48550/arxiv.1307.1565

arXiv admin note: text overlap with arXiv:1205.0498

arxiv created 2013/07/05 · arxiv updated 2013/07/08

Abstract

In this note we derive a sharp concentration inequality for the supremum of a smooth random field over a finite dimensional set. It is shown that this supremum can be bounded with high probability by the value of the field at some deterministic point plus an intrinsic dimension of the optimisation problem. As an application we prove the exponential inequality for a function of the maximal eigenvalue of a random matrix is proved.

Citations

• Penalized maximum likelihood estimation and effective dimension

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