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Asymptotic behaviour of the empirical process for exchangeable data

Author

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  • Berti, Patrizia
  • Pratelli, Luca
  • Rigo, Pietro

Abstract

Let be the space of real cadlag functions on with finite limits at ±[infinity], equipped with uniform distance, and let Xn be the empirical process for an exchangeable sequence of random variables. If regarded as a random element of , Xn can fail to converge in distribution. However, in this paper, it is shown that E*f(Xn)-->E*f(X) for each bounded uniformly continuous function f on , where X is some (nonnecessarily measurable) random element of . In view of this fact, among other things, a conjecture raised in [P. Berti, P. Rigo, Convergence in distribution of nonmeasurable random elements, Ann. Probab. 32 (2004) 365-379] is settled and necessary and sufficient conditions for Xn to converge in distribution are obtained.

Suggested Citation

  • Berti, Patrizia & Pratelli, Luca & Rigo, Pietro, 2006. "Asymptotic behaviour of the empirical process for exchangeable data," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 337-344, February.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:2:p:337-344
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    Cited by:

    1. Gianluca Cassese, 2015. "Conglomerability and representations," Working Papers 318, University of Milano-Bicocca, Department of Economics, revised 16 Dec 2015.
    2. 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.
    3. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2009. "Atomic Intersection of s-Fields and Some of Its Consequences," Quaderni di Dipartimento 096, University of Pavia, Department of Economics and Quantitative Methods.
    4. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "A Skorohod Representation Theorem for Uniform Distance," Quaderni di Dipartimento 109, University of Pavia, Department of Economics and Quantitative Methods.

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