Invariance principles for adaptive self-normalized partial sums processes.

DOI10.1016/S0304-4149(01)00096-5zbMath1059.60043MaRDI QIDQ1765994

Alfredas Račkauskas, Charles Suquet

Publication date: 25 February 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

invariance principleadaptive self-normalized partial sums processHölder space of functionsHölder weak convergence

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Functional limit theorems; invariance principles (60F17) Probability theory on linear topological spaces (60B11)

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Hölder norm test statistics for epidemic change ⋮ Limit theorems for self-normalized linear processes ⋮ A general result on almost sure central limit theorem for self-normalized sums for mixing sequences ⋮ The self-normalized Donsker theorem revisited ⋮ The stochastic heat equation as the limit of a stirring dynamics perturbed by a voter model ⋮ Process convergence of self-normalized sums of i.i.d. random variables coming from domain of attraction of stable distributions ⋮ Functional asymptotic confidence intervals for a common mean of independent random variables ⋮ Functional central limit theorems for self-normalized least squares processes in regression with possibly infinite variance data ⋮ Functional central limit theorems for self-normalized partial sums of linear processes ⋮ Donsker's theorem for self-normalized partial sums processes ⋮ Uniform asymptotic normality of self-normalized weighted sums of random variables ⋮ An extension of almost sure central limit theorem for self-normalized products of sums for mixing sequences ⋮ Functional asymptotic confidence intervals for the slope in linear error-in-variables models

Cites Work

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• Lipschitz smoothness and convergence with applications to the central limit theorem for summation processes
• Self-normalized laws of the iterated logarithm
• A Cramér type large deviation result for Student's \(t\)-statistic
• Self-normalized large deviations
• When is the Student \(t\)-statistic asymptotically standard normal?
• The Berry-Esseen bound for Student's statistic
• Limit distributions of self-normalized sums
• On the asymptotic normality of self-normalized sums
• A limit theorem for sample maxima and heavy branches in Galton–Watson trees
• On Convergence of Stochastic Processes

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