Uniform Limit Theorem and tail estimates for parametric u-statistics

E. Ostrovsky; L. Sirota

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arXiv · 1608.03310

Uniform Limit Theorem and tail estimates for parametric u-statistics

E. Ostrovsky·L. Sirota

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Abstract

We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also a non-asymptotic and non-improvable up to multiplicative constant moment and exponential tail estimates for distribution for the uniform norm of centered and naturally normed deviation of u-statistics by means of its martingale representation. Our results are formulated in a very popular and natural terms of metric entropy in the distance (distances) generated by the introduced random processes (fields).

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E. Ostrovsky, L. Sirota. 2016-08-10. Uniform Limit Theorem and tail estimates for parametric u-statistics. https://arxiv.org/abs/1608.03310

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