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Sectorial convergence of U-statistics

Anda Gadidov
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Abstract

In this note we show that almost sure convergence to zero of symmetrized U-statistics indexed by a linear sector in Z^d_+ is equivalent to convergence along the diagonal of Z^d_+, as it is considered in Lata\la and Zinn [Ann. Probab. 28 (2000) 1908-1924]. Comparisons with similar results for sums of multi-indexed i.i.d. random variables are also made.

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Anda Gadidov. 2005-03-29. Sectorial convergence of U-statistics. https://doi.org/10.1214/009117904000001080

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