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A uniform limit theorem for predictive distributions

  • Berti, Patrizia
  • Rigo, Pietro
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-44SHKCW-1/2/596f4d6200cecd5e2975a07c58db9156
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 56 (2002)
    Issue (Month): 2 (January)
    Pages: 113-120

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    Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:113-120
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    1. Berti, Patrizia & Rigo, Pietro, 1997. "A Glivenko-Cantelli theorem for exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 385-391, April.
    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. 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.
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