Abstract
Under mild conditions, a Bernstein-Hoeffding-type inequality is established for covariance invariant negatively associated random variables. The proof uses a truncation technique together with a block decomposition of the sums to allow an approximation to independence.
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References
Alam K, Saxena KML (1981) Positive dependent in multivariate distributions. Commun Statist Theor Meth A 10:1183–1196
Azuma K (1967) Weighted sums of certain dependent random variables. Tohoku Math J 19:357–369
Block HW, Savits TH, Sharked M (1982) Some concepts of negative dependence. Ann Probab 10:765–772
Bosq D (1996) Nonparametric Statistics for Stochastic Processes. Lecture Notes in Statistics, vol 110 Springer, Berlin
Carbon M (1993) Une nouvelle inegalite de grandes deviations. Applications. Publ. IRMA Lille. 32 XI
Devroye L (1991) Exponential inequalities in nonparametric estimation. In: Roussas G (eds). Nonparametric functional estimation and related topics. Kluwer, Dordrecht, pp 31–44
Joag-dev K, Proschan F (1983) Negative associated of random variables with application. Ann Statist 11:286–295
Oliveira PE (2005) An exponential inequality for associated variables. Statist Probab Lett 73:189–197
Lesigne E, Volny D (2001) Large deviations for martingales. Stochastic Process. Appl 96:143–159
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Nooghabi, H.J., Azarnoosh, H.A. Exponential inequality for negatively associated random variables. Stat Papers 50, 419–428 (2009). https://doi.org/10.1007/s00362-007-0081-4
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DOI: https://doi.org/10.1007/s00362-007-0081-4