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On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes

Authors :
Park, Jinyoung
Pham, Huy Tuan
Publication Year :
2022

Abstract

For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-$p$ setting, and answer a question of Talagrand on the analogous result for general positive empirical processes.<br />Comment: Final version, 22 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2204.10309
Document Type :
Working Paper