Uniform Limit Theorem and tail estimates for parametric u-statistics

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).

arXiv admin note: text overlap with arXiv:1602.00175

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Cited by in corpus (2)

• Moment and tail estimation for U-statistics with positive kernels
• Moment and tail estimates and Banach space valued Non-Central Limit Theorem (NCLT) for sums of multi-indexed random variables, processes and fields