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On complete convergence of triangular arrays of independent random variables

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  • Berkes, István
  • Weber, Michel

Abstract

Given a triangular array a={an,k,1[less-than-or-equals, slant]k[less-than-or-equals, slant]kn,n[greater-or-equal, slanted]1} of positive reals, we study the complete convergence property of for triangular arrays of independent random variables. In the Gaussian case we obtain a simple characterization of density type. Using Skorohod representation and Gaussian randomization, we then derive sufficient criteria for the case when Xn,k are in Lp, and establish a link between the Lp-case and L2p-case in terms of densities. We finally obtain a density type condition in the case of uniformly bounded random variables.

Suggested Citation

  • Berkes, István & Weber, Michel, 2007. "On complete convergence of triangular arrays of independent random variables," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 952-963, June.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:10:p:952-963
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    References listed on IDEAS

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    1. Li, Deli & Bhaskara Rao, M. & Wang, Xiangchen, 1992. "Complete convergence of moving average processes," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 111-114, May.
    2. Ahmed, S. Ejaz & Antonini, Rita Giuliano & Volodin, Andrei, 2002. "On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 185-194, June.
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    Cited by:

    1. Gourieroux, Christian & Jasiak, Joann, 2010. "Inference for Noisy Long Run Component Process," MPRA Paper 98987, University Library of Munich, Germany.
    2. Szewczak, Zbigniew S., 2015. "A moment maximal inequality for dependent random variables," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 129-133.

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