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A uniform limit theorem for predictive distributions


  • Berti, Patrizia
  • Rigo, Pietro


Let be a filtration, {Xn} an adapted sequence of real random variables, and {[alpha]n} a predictable sequence of non-negative random variables with [alpha]1>0. Set and define the random distribution functions and . Under mild assumptions on {[alpha]n}, it is shown that , a.s. on the set {Fn or Bn convergesuniformly}. Moreover, conditions are given under which Fn converges uniformly with probability 1.

Suggested Citation

  • Berti, Patrizia & Rigo, Pietro, 2002. "A uniform limit theorem for predictive distributions," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 113-120, January.
  • Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:113-120

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    References listed on IDEAS

    1. Hanson, D. L. & Li, Gang, 1997. "A note on the empirical distribution of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 337-340, June.
    2. Etemadi, N., 1983. "Stability of sums of weighted nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 361-365, June.
    3. Berti, Patrizia & Rigo, Pietro, 1997. "A Glivenko-Cantelli theorem for exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 385-391, April.
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    Cited by:

    1. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "Limit Theorems for Empirical Processes Based on Dependent Data," Quaderni di Dipartimento 132, University of Pavia, Department of Economics and Quantitative Methods.
    2. Patrizia Berti & Irene Crimaldi & Luca Pratelli & Pietro Rigo, 2009. "Rate of Convergence of Predictive Distributions for Dependent Data," Quaderni di Dipartimento 091, University of Pavia, Department of Economics and Quantitative Methods.


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