A Probabilistic Inequality Related to Negative Definite Functions

Publikation: Beitrag in Buch/Konferenzbericht/Sammelband/GutachtenBeitrag in Buch/Sammelband/GutachtenBeigetragenBegutachtung

Beitragende

Abstract

We prove that for any pair of i.i.d. random vectors X,Y in (formula presented) and any real-valued continuous negative definite function (formula presented) the inequality(formula presented) holds. In particular, for (formula presented) and the Euclidean norm (formula presented) one has (formula presented) The latter inequality is due to A. Buja et al. [4] where it is used for some applications in multivariate statistics. We show a surprising connection with bifractional Brownian motion and provide some related counter-examples.

Details

OriginalspracheEnglisch
TitelHigh Dimensional Probability VI. The Banff Volume.
Herausgeber (Verlag)Birkhauser Verlag Basel
Seiten73-80
Seitenumfang8
PublikationsstatusVeröffentlicht - 2013
Peer-Review-StatusJa

Publikationsreihe

ReiheProgress in probability : PP
Band66
ISSN1050-6977

Schlagworte

Schlagwörter

  • Bernstein functions, Bifractional Brownian motion, moment inequalities, negative definite functions