Upper bounds on product and multiplier empirical processes

Shahar Mendelson

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)

Abstract

We study two empirical processes of special structure: firstly, the centred multiplier process indexed by a class F, f→|∑i=1 Nif(Xi)−Eξf)|, where the i.i.d. multipliers (ξi)i=1 N need not be independent of (Xi)i=1 N, and secondly, (f,h)→|∑i=1 N(f(Xi)h(Xi)−Efh)|, the centred product process indexed by the classes F and H. We use chaining methods to obtain high probability upper bounds on the suprema of the two processes using a natural variation of Talagrand's γ-functionals.

Original languageEnglish
Pages (from-to)3652-3680
Number of pages29
JournalStochastic Processes and their Applications
Volume126
Issue number12
DOIs
Publication statusPublished - 1 Dec 2016
Externally publishedYes

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