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Weak convergence of stochastic processes indexed by smooth functions

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  • Arcones, Miguel A.

Abstract

We give some easy methods to check sufficient conditions for the weak convergence of stochastic processes indexed by smooth functions. The main condition is a moment condition on the increments of the process. We apply this to empirical processes and U-processes in the independent identically distributed case. We also consider empirical processes under different types of dependence conditions.

Suggested Citation

  • Arcones, Miguel A., 1996. "Weak convergence of stochastic processes indexed by smooth functions," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 115-138, March.
    • Handle: RePEc:eee:spapps:v:62:y:1996:i:1:p:115-138
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    References listed on IDEAS

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    1. Andrews, Donald W. K., 1991. "An empirical process central limit theorem for dependent non-identically distributed random variables," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 187-203, August.
    2. Arcones, Miguel A., 1994. "The central limit theorem for U-processes indexed by Hölder's functions," Statistics & Probability Letters, Elsevier, vol. 20(1), pages 57-62, May.
    3. van der Vaart, Aad, 1994. "Bracketing smooth functions," Stochastic Processes and their Applications, Elsevier, vol. 52(1), pages 93-105, August.
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