Some finite sample properties of negatively dependent random variables

Author:
Alessio Farcomeni

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **77** (2007).

Journal:
Theor. Probability and Math. Statist. **77** (2008), 155-163

MSC (2000):
Primary 60E15, 47N30

DOI:
https://doi.org/10.1090/S0094-9000-09-00754-6

Published electronically:
January 21, 2009

MathSciNet review:
2432779

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss some finite sample properties of vectors of negatively dependent random variables. We extend some inequalities, widely used for independent random variables, and some basic tools such as the symmetrization lemma, to the case of negatively dependent random variables.

**1.**M. D. Amini and A. Bozorgnia,*Complete convergence for negatively dependent random sequences*, Journal of Applied Mathematics and Stochastic Analysis**16**(2003), 121-126. MR**1989578 (2004j:60037)****2.**H. W. Block, T. H. Savits, and M. Shaked,*Some concepts of negative dependence*, The Annals of Probability**10**(1982), 765-772. MR**659545 (83i:60015)****3.**J. D. Esary, F. Proschan, and D. W. Walkup,*Association of random variables, with applications*, The Annals of Mathematical Statistics**38**(1967), 1466-1474. MR**0217826 (36:915)****4.**J. D. Kumar and F. Proschan,*Negative association of random variables with applications*, The Annals of Statistics**11**(1983), 286-295. MR**684886 (85d:62058)****5.**C. McDiarmid,*On the method of bounded differences*, Surveys in Combinatorics, Cambridge University Press, 1989, pp. 148-188. MR**1036755 (91e:05077)****6.**A. Volodin,*On the Kolmogorov exponential inequality for negatively dependent random variables*, Pakistan Journal of Statistics**18**(2002), 249-253. MR**1944611 (2003k:60053)****7.**Y. L. Tong,*Probability Inequalities in Multivariate Distributions*, Academic Press, 1980. MR**572617 (82k:60038)**

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Additional Information

**Alessio Farcomeni**

Affiliation:
University of Rome “La Sapienza”, Piazzale Aldo Moro 5, 00185 Rome, Italy

Email:
alessio.farcomeni@uniroma1.it

DOI:
https://doi.org/10.1090/S0094-9000-09-00754-6

Keywords:
Negative dependence,
association,
Hoeffding inequality,
exponential tail inequality,
bounded difference inequality,
empirical distribution,
symmetrization lemma

Received by editor(s):
August 10, 2006

Published electronically:
January 21, 2009

Article copyright:
© Copyright 2009
American Mathematical Society