Weak Convergence of $U$-Statistics and Von Mises' Differentiable Statistical Functions

DOI10.1214/aoms/1177692698zbMath0238.62057OpenAlexW2041493931MaRDI QIDQ5649293

Pranab Kumar Sen, Rupert G. jun. Miller

Publication date: 1972

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

Full work available at URL: https://doi.org/10.1214/aoms/1177692698

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Convergence of probability measures (60B10)

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Cumulative processes: Linear combinations of order statistics and percentiles ⋮ U-Statistics in Sequential Tests and Change Detection ⋮ An invariance principle for reduced U-statistics ⋮ A note on invariance principles for v. Mises' statistics ⋮ A Nonparametric Sequential Point Estimator ⋮ Weak and strong representations for trimmed U-statistics ⋮ Strong laws for randomly indexed U-statistics ⋮ REPEATED SIGNIFICANCE TESTS IN FREQUENCY AND TIME DOMAINS* ⋮ Subsampling based inference for \(U\) statistics under thick tails using self-normalization ⋮ Weak invariance principle for finite-population U-statistics ⋮ On weak approximations of \(U\)-statistics ⋮ An invariance principle for U-statistics in simple random sampling without replacement ⋮ Invariance principles for U-statistics and von Mises functionals ⋮ Two-stage testing whether new is better than used ⋮ Asymptotic normality for -dependent and constrained -statistics, with applications to pattern matching in random strings and permutations ⋮ Limiting behavior of regular functionals of empirical distributions for stationary *-mixing processes ⋮ The weak convergence for self-normalized \(U\)-statistics with dependent samples ⋮ Maximal inequalities and convergence results for generalized U- statistics ⋮ Asymptotic theorems for kernel U-quantiles ⋮ Limiting behavior of U-statistics for stationary, absolutely regular processes ⋮ Renewal theory for asymmetric \(U\)-statistics ⋮ Weighted approximations for Studentized \(U\)-statistics ⋮ Asymptotic properties of linear combinations of U-statistics with degenerate kernels ⋮ On functional laws of the iterated logarithm ⋮ A repeated significance test for new better than used ⋮ Invariance principles for von Mises and U-statistics ⋮ Life and Work of Bhaskar Kumar Ghosh ⋮ On the weak convergence of U-statistic processes, and of the empirical process ⋮ Asymptotic Behavior of Optimal Weighting in Generalized Self‐Normalization for Time Series ⋮ Weak convergence and relative compactness of martingale processes with applications to some nonparametric statistics ⋮ On U-statistics and v. mise? statistics for weakly dependent processes ⋮ Invariance principles for stochastic area and related stochastic integrals ⋮ \(U\)-statistics on a lattice of i. i. d. random variables ⋮ Nonparametric Sequential Comparison of Two Treatments with Random Allocation ⋮ Some invariance principles for rank statistics for testing independence ⋮ Functional convergence of sequential \(U\)-processes with size-dependent kernels

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