Some finite sample properties of negatively dependent random variables
Author:
Alessio Farcomeni
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
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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.
References
- M. Amini D. and A. Bozorgnia, Complete convergence for negatively dependent random variables, J. Appl. Math. Stochastic Anal. 16 (2003), no. 2, 121–126. MR 1989578, DOI https://doi.org/10.1155/S104895330300008X
- Henry W. Block, Thomas H. Savits, and Moshe Shaked, Some concepts of negative dependence, Ann. Probab. 10 (1982), no. 3, 765–772. MR 659545
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References
- 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)
- 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)
- 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)
- 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)
- C. McDiarmid, On the method of bounded differences, Surveys in Combinatorics, Cambridge University Press, 1989, pp. 148–188. MR 1036755 (91e:05077)
- A. Volodin, On the Kolmogorov exponential inequality for negatively dependent random variables, Pakistan Journal of Statistics 18 (2002), 249–253. MR 1944611 (2003k:60053)
- 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
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
