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Moderate deviations for triangular arrays

  • GAO Zhen-Long
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  • School of Mathematical Sciences, Graduate University, Chinese Acadmey of Sciences, Beijing 100049, China

Received date: 2010-01-29

  Revised date: 2010-06-15

  Online published: 2011-01-20

Abstract

Using the method of truncation,we get the moderate deviations for triangular arrays of random variables {Xn,j;1≤j≤kn,n≥1} under some conditions of tail probability,where {kn;n≥1} is a sequence of strictly increasing positive integers and for any fixed n,{Xn,j;1≤j≤kn} are i.i.d.

Cite this article

GAO Zhen-Long . Moderate deviations for triangular arrays[J]. Journal of University of Chinese Academy of Sciences, 2011 , 28(1) : 5 -11 . DOI: 10.7523/j.issn.2095-6134.2011.1.002

References


[1] Acosta A D.Moderate deviations and associated Laplace approximations for sums of independent random vectors
[J].Trans Amer Math Soc,1992,329(1):357-375.

[2] Arcones M A.Moderate deviations of empirical processes
[J].Stochastic Inequalities and Applications,2003,56:189-212.

[3] Eichelsbacher P,L we M.Moderate deviations for i.i.d.random variables
[J].Probab Statist,2003,7(1):209-218.

[4] Davis J A.Convergence rates for probabilities of moderate deviations
[J].Ann Math Statist,1968,39(6):2016-2028.

[5] Li D L,Wang X C,Rao M B.Some results on convergence rates for probabilities of moderate deviations for sums of random variables
[J].Internat J Math Sci,1992,15(3):481- 498.

[6] Merlevède F,Peligrad M.Functional moderate deviations for triangular arrays and applications
[J].Alea,2009,5(1):3-20.

[7] Frolov A N.One one-sided strong laws for large increments of sums
[J].Statist Probab Lett,1998,37(1):155-165.

[8] Frolov A N.On probabilities of moderate deviations of sums of independent random variables
[J].J Math Sci,2005,127(1):1787-1796.

[9] Petrov V V.On probabilities of moderate deviations
[J].Zap Nauchn Semin POMI,1999,260(1):214-217.

[10] Dembo A,Zeitouni O.Large deviations techniques and application
[M].2nd ed.New York:Springer,1998:44,131.

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