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A note on limit theorems for perturbed empirical processes

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  • Yukich, J. E.

Abstract

Let Xi, i[greater-or-equal, slanted] 1, be a sequence of i.i.d.k-valued random variables with common distribution P. Let Hnn[greater-or-equal, slanted]1, be a sequence of distribution functions (d.f.) such that , where H0 is the d.f. of the unit mass at zero. The perturbed empirical d.f. is defined by denotes the associated perturbed empirical probability measure. Strong laws of large numbers and weak invariance principles are obtained for the perturbed empirical processes , , where denotes a class of functions on k. The results extend and generalize those of Winter and Yamato and have applications to non-parametric density estimation.

Suggested Citation

  • Yukich, J. E., 1989. "A note on limit theorems for perturbed empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 163-173, October.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:1:p:163-173
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    Citations

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    Cited by:

    1. Majid Mojirsheibani, 2006. "A Note on the Strong Approximation of the Smoothed Empirical Process of α-mixing Sequences," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 97-107, May.
    2. Bouzebda, Salim & Slaoui, Yousri, 2022. "Nonparametric recursive method for moment generating function kernel-type estimators," Statistics & Probability Letters, Elsevier, vol. 184(C).
    3. Faugeras, Olivier & Rüschendorf, Ludger, 2019. "Functional, randomized and smoothed multivariate quantile regions," TSE Working Papers 19-1039, Toulouse School of Economics (TSE), revised Jun 2021.

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