Central limit theorems for a class of symmetric statistics

DOI10.1017/S0305004100061168zbMath0563.60025OpenAlexW2053881317MaRDI QIDQ3676892

Neville C. Weber

Publication date: 1983

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100061168

zbMATH Keywords

central limit theoremsU-statistic

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

Related Items (14)

A central limit theorem for generalized quadratic forms ⋮ Functional limit theorems for random multilinear forms ⋮ Asymptotic normality of quadratic estimators ⋮ Asymptotic theory of U-statistics ⋮ Limit theorems for short distances in \(\mathbb{R}^m\) ⋮ Weak convergence of row and column exchangeable arrays ⋮ A central limit theorem for generalized multilinear forms ⋮ Nonparametric estimators for the probability of ruin ⋮ Testing multivariate uniformity based on random geometric graphs ⋮ Quantitative CLTs for symmetric \(U\)-statistics using contractions ⋮ Short distances on the line ⋮ A class of \(U\)-statistics and asymptotic normality of the number of \(k\)- clusters ⋮ An Asymptotic Characterization of Finite Degree U-statistics With Sample Size-Dependent Kernels: Applications to Nonparametric Estimators and Test Statistics ⋮ Estimation of entropy-type integral functionals

Cites Work

• Unnamed Item
• Asymptotic normality of the number of small distances between random points in a cube
• Rates of Poisson convergence for U-statistics
• Short distances, flat triangles and Poisson limits
• Central limit theorems for martingales and for processes with stationary increments using a Skorokhod representation approach
• A Class of Statistics with Asymptotically Normal Distribution

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