Asymptotics for self-normalized random products of sums of i.i.d. random variables

DOI10.1016/j.jmaa.2006.12.085zbMath1121.60020OpenAlexW1995364747MaRDI QIDQ996910

Tian-Xiao Pang, Kyo-Shin Hwang, Zheng Yan Lin

Publication date: 19 July 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.12.085

zbMATH Keywords

lognormal distributiondomain of attraction of the normal lawi.i.d. random variablesself-normalized products

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (10)

An improved result in almost sure central limit theorem for self-normalized products of partial sums ⋮ A general result on almost sure central limit theorem for self-normalized sums for mixing sequences ⋮ An almost sure central limit theorem for self-normalized products of sums of i.i.d. random variables ⋮ Limit distribution for products of sums of partial sums of linear processes generated by NSD sequence ⋮ An almost sure central limit theorem for self-normalized weighted sums ⋮ Almost sure central limit theorem for self-normalized products of partial sums of negatively associated sequences ⋮ Moderate deviations principle for products of sums of random variables ⋮ A weak invariance principle for self-normalized products of sums of mixing sequences ⋮ The moderate deviation principle for self-normalized sums of sums of i.i.d. random variables ⋮ An extension of almost sure central limit theorem for self-normalized products of sums for mixing sequences

Cites Work

• Self-normalized laws of the iterated logarithm
• The asymptotic distribution of sums of records
• Studentized increments of partial sums
• When is the Student \(t\)-statistic asymptotically standard normal?
• Limit distributions for products of sums.
• Donsker's theorem for self-normalized partial sums processes
• Asymptotics for products of sums and \(U\)-statistics
• A note on asymptotic distribution of products of sums
• The Berry-Esseen bound for Student's statistic
• On the central limit theorem for the sum of a random number of independent random variables
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