Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 11 (2006) > Paper 24 open journal systems 


A multivariate version of Hoeffding's inequality

Peter Major, Alfred Renyi Mathematical Institute of the Hungarian Academy of Sciences


Abstract
In this paper a multivariate version of Hoeffding's inequality is proved about the tail distribution of homogeneous polynomials of Rademacher functions with an optimal constant in the exponent of the upper bound. The proof is based on an estimate about the moments of homogeneous polynomials of Rademacher functions which can be considered as an improvement of Borell's inequality in a most important special case.


Full text: PDF | PostScript

Pages: 220-229

Published on: October 9, 2006


Bibliography
  1. Bonami, A. Étude des coefficients de Fourier des fonctions de $L^p(G)$. Ann. Inst. Fourier (Grenoble) 20 (1970), 335--402 Math. Review 44#727
  2. Borell, C. On the integrability of Banach space valued Walsh polynomials. Séminaire de Probabilités XIII, Lecture Notes in Math. 721 Springer, Berlin. (1979) 1--3. Math. Review 81g:42026
  3. Dudley, R. M. Uniform Central Limit Theorems. Cambridge University Press, Cambridge U.K. (1998) Math. Review 2000k:60050
  4. Dynkin, E. B. and Mandelbaum, A. (1983) Symmetric statistics, Poisson processes and multiple Wiener integrals. Annals of Statistics 11 (1983), 739--745 Math. Review 85b;60015
  5. Gross, L. (1975) Logarithmic Sobolev inequalities. Amer. J. Math. 97, (1975) 1061--1083 Math. Review 54#8263
  6. Ito K. Multiple Wiener integral. J. Math. Soc. Japan 3 (1951), 157--164 Math. Review 13.364a
  7. Janson, S. Gaussian Hilbert spaces. Cambridge Tracts in Mathematics, 129. Cambridge University Press, Cambridge (1997) Math. Review 99f:60082
  8. Major, P. Multiple Wiener--It integrals. Lecture Notes in Mathematics 849, Springer Verlag, Berlin Heidelberg, New York, (1981) Math. Review 82i:60099
  9. Major, P. Tail behaviour of multiple random integrals and $U$-statistics. Probability Reviews. (2005) 448--505 Math. Review number not available.
  10. Major, P. An estimate on the maximum of a nice class of stochastic integrals. Probability Theory and Related Fields., 134, (2006) 489--537 Math. Review number not available.
  11. Major, P. On a multivariate version of Bernstein's inequality. Submitted to Journal of Electronic Probability (2006) Math. Review number not available.
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X