Weak Convergence of Self-normalized Partial Sums Processes

DOI10.1007/978-1-4939-3076-0_1zbMath1368.60047arXiv1204.2074OpenAlexW2495300095MaRDI QIDQ5272938

Zhishui Hu, Miklós Csörgő

Publication date: 5 July 2017

Published in: Asymptotic Laws and Methods in Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.2074

zbMATH Keywords

weak convergenceself-normalizationpartial sums processes

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items

The self-normalized Donsker theorem revisited

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On weighted approximations in \(D[0,1\) with applications to self-normalized partial sum processes]
• Functional asymptotic confidence intervals for the slope in linear error-in-variables models
• Infinite limits and infinite limit points of random walks and trimmed sums
• Self-normalized large deviations
• When is the Student \(t\)-statistic asymptotically standard normal?
• Donsker's theorem for self-normalized partial sums processes
• Limit distributions of Studentized means.
• Functional asymptotic confidence intervals for a common mean of independent random variables
• Limit distributions of self-normalized sums
• Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation
• On the asymptotic normality of self-normalized sums
• Towards a universal self-normalized moderate deviation
• Self-Normalized Processes
• Notes on Extreme and Self-Normalised Sums from the Domain of Attraction of a Stable Law
• A limit theorem for sample maxima and heavy branches in Galton–Watson trees
• Student's t-Test Under Symmetry Conditions
• Canonical representations and convergence criteria for processes with interchangeable increments
• Probabilistic Symmetries and Invariance Principles
• The Influence of the Maximum Term in the Addition of Independent Random Variables