Order of magnitude bounds for expectations of \(\Delta_2\)-functions of nonnegative random bilinear forms and generalized \(U\)-statistics

DOI10.1214/aop/1024404521zbMath0895.60018OpenAlexW2141338394MaRDI QIDQ1370235

Krzysztof Nowicki, Michael J. Klass

Publication date: 20 September 1998

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1024404521

zbMATH Keywords

growth conditionrandom bilinear formsarray of nonnegative functionsgeneralized \(U\)-statisticsKhinchin-type inequalities

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50) (L^p)-limit theorems (60F25)

Related Items (5)

A symmetrization-desymmetrization procedure for uniformly good approximation of expectations involving arbitrary sums of generalized \(U\)-statistics. ⋮ On extremal distributions and sharp \(L_p\)-bounds for sums of multilinear forms ⋮ Exponential inequalities for the supremum of some counting processes and their square martingales ⋮ Another approach to Brownian motion ⋮ Sub-Bernoulli functions, moment inequalities and strong laws for nonnegative and symmetrized \(U\)-statistics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of quadratic forms in p-stable random variables and \(\theta _ p\)-radonifying operators
• Decoupling inequalities for multilinear forms in independent symmetric random variables
• On a p-stable multiple integral. I, II
• Invertibility of ``large submatrices with applications to the geometry of Banach spaces and harmonic analysis
• A method of approximating expectations of functions of sums of independent random variables
• Order-of-magnitude bounds for expectations involving quadratic forms
• Decoupling inequalities for the tail probabilities of multivariate \(U\)- statistics
• On the almost sure minimal growth rate of partial sum maxima
• Bounds on the Expectation of Functions of Martingales and Sums of Positive RV's in Terms of Norms of Sums of Independent Random Variables

This page was built for publication: Order of magnitude bounds for expectations of \(\Delta_2\)-functions of nonnegative random bilinear forms and generalized \(U\)-statistics