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On the exponential inequality for negative dependent sequence

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Abstract

We show an exponential inequalityfor negatively associated and strictly stationary random variablesreplacing an uniform boundedness assumption by the existence ofLaplace transforms. To obtain this result we use a truncationtechnique together with a block decomposition of the sums. We alsoidentify a convergence rate for the strong law of large number.

참고문헌 (10)

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  2. } In, "{Exponential inequalities in nonparametricestimation", (nparametric functionalestimation and related topics), pp.31~ (1991), Kluwer Academic Publishers
  3. } Ann, "{ Negative association ofrandom variables with applications", pp.286~ (1983)
  4. E. Lesigne, "Large deviationsfor martingales", 96, pp.143~159 (2001)
  5. H. Y. Liang, "Complete convergence for weighted sums ofnegatively associated ranldom variables", 48, pp.317~325 (2000)
  6. Matula, "{ A note on the almost sure convergence ofsums of negatively dependent random variables", pp.209~ (1992)
  7. Newman, "Inequalities in Statistics and Probability", pp.127~ (1984), IMS LecturesNotes-Monograph Series textbf{5}
  8. G. G. Roussas, "Exponential probability inequalitieswith some applications, In:Ferguson, T. S., Shapely, L. S.,MacQueen, J. B.(Ed.),Statistics, Probability and Game Theory. IMSLecture Notes-Monograph Series", 30, pp.303~309 (1996), IMSLecture Notes-Monograph Series
  9. Q. M. Shao, "A comparison theorem on maximuminequalities between negatively associated and independent randomvariables", 13, pp.343~356 (2000)
  10. Q. M. Shao, "The law of the iterated logarithmfor negatively associated random variables", 83, pp.139~148 (1999)

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