\(U\)-statistics on a lattice of i. i. d. random variables

DOI10.1016/S0167-7152(98)00111-4zbMath0936.60019MaRDI QIDQ1305293

Tasos C. Christofides, Robert J. Serfling

Publication date: 9 May 2000

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Nonparametric estimation (62G05) Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (1)

Central limit theorem for dependent multidimensionally indexed random variables.

Cites Work

• Maximal inequalities for multidimensionally indexed submartingale arrays
• Generalized order statistics, Bahadur representations, and sequential nonparametric fixed-width confidence intervals
• . strong law of large numbers for \(U\)-statistics
• The weak law of large numbers for arrays
• Convergence rates for U-statistics and related statistics
• Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices
• Approximation Theorems of Mathematical Statistics
• An elementary proof of the strong law of large numbers
• Marcinkiewicz strong laws of large numbers and convergence rates for arrays of independent random elements in banach spaces
• Asymptotic Properties of U-Statistics
• The Invariance Principle for a Lattice of Random Variables
• Sequential Confidence Intervals Based on Rank Tests
• Inequalities with Applications to the Weak Convergence of Random Processes with Multi-Dimensional Time Parameters
• Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions
• A Class of Statistics with Asymptotically Normal Distribution
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