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Limit Theorems for Empirical Processes Based on Dependent Data

Author

Listed:
  • Patrizia Berti

    (Department of Mathematics, University of Modena and Reggio Emilia)

  • Luca Pratelli

    (Accademia Navale di Livorno)

  • Pietro Rigo

    (Department of Economics and Quantitative Methods, University of Pavia)

Abstract

Empirical processes for non ergodic data are investigated under uniform distance. Some CLTs, both uniform and non uniform, are proved. In particular, conditions for Bn = n^(1/2) (µn - bn) and Cn = n^(1/2) (µn - an) to converge in distribution are given, where µn is the empirical measure, an the predictive measure, and bn = 1/n sum (ai) for i=0 to n-1. Such conditions can be applied to any adapted sequence of random variables. Various examples and a characterization of conditionally identically distributed sequences are given as well.

Suggested Citation

  • 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.
    • Handle: RePEc:pav:wpaper:132
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    References listed on IDEAS

    as
    1. Patrizia Berti & Irene Crimaldi & Luca Pratelli & Pietro Rigo, 2010. "A Central Limit Theorem and Its Applications to Multicolor Randomly Reinforced Urns," Quaderni di Dipartimento 112, University of Pavia, Department of Economics and Quantitative Methods.
    2. Etemadi, N. & Kaminski, M., 1996. "Strong law of large numbers for 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 245-250, July.
    3. 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.
    4. Berti, Patrizia & Rigo, Pietro, 2002. "A uniform limit theorem for predictive distributions," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 113-120, January.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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