Invariance principle under self-normalization for nonidentically distributed random variables
type: Item
instance of: scholarly article
title: Invariance principle under self-normalization for nonidentically distributed random variables
zbMATH Open document ID: 1035.60019
DOI: 10.1023/A:1025820212601
published in: Acta Applicandae Mathematicae
publication date: 2003-12-04T00:00:00Z
review text: The authors consider the adaptive process \(V^{-1}_n\zeta_n\) of self-normalized partial sums \(S_k\) of independent random variables \(X_j\), defined by linear interpolation between the points \((V^2_k/V^2_n, S_k/V_n)\), \(k\leq n\), where \(V^2_k=\sum_{j\leq k}X^2_j\). They prove that if the \(X_k\)'s are symmetric, \(V^{-1}_n\zeta_n\) converges weakly to the Brownian motion \(W\) in each Hölder space supporting \(W\) if \(\max_{1\leq k\leq n}X^2_k/V^2_n@>P>>0\) as \(n\to\infty.\)
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 2012903
zbMATH Keywords: invariance principle
zbMATH Keywords: Hölder space
zbMATH Keywords: Brownian motion
author: Alfredas Račkauskas
author: Charles Suquet
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
full work available at URL: a:1025820212601
OpenAlex ID: W64162411
description: scientific article; zbMATH DE number 2012903