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Uniform CLT for empirical process

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  • Ben Hariz, Samir

Abstract

Empirical processes indexed by classes of functions based on dependent observations are considered. Sufficient conditions in order to satisfy stochastic equicontinuity are given. The derived conditions are in terms of bracketing numbers with respect to a norm arising from a Rosenthal type moment inequality satisfied by the process. The application involves mixing sequences and improves on the result of Andrews and Pollard (Int. Statist. Rev. 62 (1) (1994) 119) for strong mixing, Shao and Yu (Ann. Probab. 24 (4) (1996) 2098) for [rho]-mixing sequences, and Csörgo and Mielniczuk (Probab. Theory Relat. Fields 104 (1) (1996) 15) for functions of Gaussian sequences.

Suggested Citation

  • Ben Hariz, Samir, 2005. "Uniform CLT for empirical process," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 339-358, February.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:2:p:339-358
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    References listed on IDEAS

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    1. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    2. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
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    Cited by:

    1. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org, revised Jan 2023.
    2. Jean‐Jacques Forneron, 2023. "A Sieve‐SMM Estimator for Dynamic Models," Econometrica, Econometric Society, vol. 91(3), pages 943-977, May.

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