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Weak invariance principles for weightedU-statistics

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Abstract

We prove that the distribution of a properly normalized weightedU-statisticU n in i.i.d. random variables is “close” to the distribution of a certain functionV n in i.i.d. standardized Gaussian random variables in the sense that their Lévy-Prokhorov distance tends to zero asn→∞. This property is then used to determine the limit laws ofU n under special assumptions on the kernel function. This generalizes a method due to Rotar' who proved similar results for random multilinear forms.

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  1. ISOR, Victoria University of Wellington, Wellington, New Zealand

    Thomas Mikosch

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Mikosch, T. Weak invariance principles for weightedU-statistics. J Theor Probab 7, 147–173 (1994). https://doi.org/10.1007/BF02213365

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  • DOI: https://doi.org/10.1007/BF02213365

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