| Título: | On a Multivariate Version of Bernstein's Inequality |
| Autores: | Major, Peter; Renyi Mathematical Institute of the Hungarian Academy of Sciences |
| Fecha: | 2007-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Bernstein inequality, (degenerate) U-statistics, Wiener--It^o integrals, diagram formula, moment estimates Primary 60E15, 60F10, Secondary 60H99 |
| Descripción: | We prove such a multivariate version of Bernstein's inequality about the tail distribution of degenerate $U$-statistics which is an improvement of some former results. This estimate will be compared with an analogous bound about the tail distribution of multiple Wiener-Ito integrals. Their comparison shows that our estimate is sharp. The proof is based on good estimates about high moments of degenerate $U$-statistics. They are obtained by means of a diagram formula which enables us to express the product of degenerate $U$-statistics as the sum of such expressions. |
| Idioma: | No aplica |
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