A Probabilistic Inequality Related to Negative Definite Functions
Publikation: Beitrag in Buch/Konferenzbericht/Sammelband/Gutachten › Beitrag in Buch/Sammelband/Gutachten › Beigetragen › Begutachtung
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
Originalsprache | Englisch |
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Titel | High Dimensional Probability VI. The Banff Volume. |
Herausgeber (Verlag) | Birkhauser Verlag Basel |
Seiten | 73-80 |
Seitenumfang | 8 |
Publikationsstatus | Veröffentlicht - 2013 |
Peer-Review-Status | Ja |
Publikationsreihe
Reihe | Progress in probability : PP |
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Band | 66 |
ISSN | 1050-6977 |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- Bernstein functions, Bifractional Brownian motion, moment inequalities, negative definite functions