Moment and tail estimation for U-statistics with positive kernels

2018/01/20 by E. Ostrovsky, Ostrovsky, E., L. Sirota +1
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1801.07588

openalex publication_date 2018/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deduce the non-asymptotical (bilateral) estimates for moment inequalities for multiple sums of non-negative (more precisely, non-negative) independent random variables, on the other words, the well known U or V-statistics. Our consideration based on the correspondent estimates for the one-dimensional case by means of the so-called degenerate approximation. We apply also the theory of Bell functions as well as the properties of the Poisson distribution and the theory of the so-called Grand Lebesgue Spaces (GLS).

Citations

• Schlomilch and Bell Series for Bessel's Functions, with Probabilistic Applications
• Relations between exponential tails, moments and moment generating functions for random variables and vectors

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