Moment and tail estimation for U-statistics with positive kernels
arXiv:1801.07588
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).
arXiv admin note: text overlap with arXiv:1710.05235
References in corpus (5)
- 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
- Sharp moment estimates for polynomial martingales
- Uniform Limit Theorem and tail estimates for parametric u-statistics
- Non-asymptotic estimation for Bell function, with probabilistic applications