Uniform Limit Theorem and tail estimates for parametric u-statistics

2016/08/10 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1608.03310

arXiv admin note: text overlap with arXiv:1602.00175

arxiv created 2016/08/10 · openalex publication_date 2016/08/10 · arxiv updated 2016/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

Citations

• Schlomilch and Bell Series for Bessel's Functions, with Probabilistic Applications
• Sharp moment estimates for polynomial martingales
• Sharp moment and exponential tail estimates for U-statistics

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