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A Weak Invariance Principle for Weighted U-Statistics with Varying Kernels

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  • Mikosch, T.

Abstract

We prove limit theorems of functional type for weighted U-statistics with varying kernel. In particular, we show that the Lévy-Prokhorov distance between these processes un and certain processes vn constructed from i.i.d. standard normal variables converges to zero. Limit results for un follow then from the corresponding ones for vn.

Suggested Citation

  • Mikosch, T., 1993. "A Weak Invariance Principle for Weighted U-Statistics with Varying Kernels," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 82-102, October.
    • Handle: RePEc:eee:jmvana:v:47:y:1993:i:1:p:82-102
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    Cited by:

    1. Francesco Bravo & Ba M. Chu & David T. Jacho-Chávez, 2017. "Semiparametric estimation of moment condition models with weakly dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 108-136, January.
    2. Rauf Ahmad, M. & Pavlenko, Tatjana, 2018. "A U-classifier for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 269-283.
    3. Robins, James M. & Li, Lingling & Tchetgen, Eric Tchetgen & van der Vaart, Aad, 2016. "Asymptotic normality of quadratic estimators," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3733-3759.

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