\(U\)-statistics on a lattice of i. i. d. random variables
type: Item
instance of: scholarly article
title: \(U\)-statistics on a lattice of i. i. d. random variables
zbMATH Open document ID: 0936.60019
DOI: 10.1016/S0167-7152(98)00111-4
author: Tasos C. Christofides
author: Robert J. Serfling
published in: Statistics \& Probability Letters
publication date: 2000-05-09T00:00:00Z
review text: The authors extend several (most?) classical limit theorems for sums of i.i.d. random variables to the case of \(U\)-statistics based on multidimensionally indexed i.i.d. random variables. Martingale properties and an a.s. representation are essential ingredients.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1346171
reviewed by: Allan Gut
MaRDI profile type: Publication
cites work: Q5812603
cites work: Q5560061
cites work: Q5623011
cites work: Generalized order statistics, Bahadur representations, and sequential nonparametric fixed-width confidence intervals
cites work: Q4040465
cites work: . strong law of large numbers for \(U\)-statistics
cites work: Maximal inequalities for multidimensionally indexed submartingale arrays
cites work: Q5807151
cites work: An elementary proof of the strong law of large numbers
cites work: Sequential Confidence Intervals Based on Rank Tests
cites work: Convergence rates for U-statistics and related statistics
cites work: Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices
cites work: The weak law of large numbers for arrays
cites work: A Class of Statistics with Asymptotically Normal Distribution
cites work: Q5612192
cites work: Q3909741
cites work: Q3670281
cites work: The Invariance Principle for a Lattice of Random Variables
cites work: Q3999009
cites work: Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions
cites work: Approximation Theorems of Mathematical Statistics
cites work: Asymptotic Properties of U-Statistics
cites work: Marcinkiewicz strong laws of large numbers and convergence rates for arrays of independent random elements in banach spaces
cites work: Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters
cites work: Q5808590
description: scientific article; zbMATH DE number 1346171