Iterated logarithm type behavior for weighted sums of i.i.d. random variables

Deli Li, Yongcheng Qi, Andrew Rosalsky

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

For a sequence of i.i.d. mean 0 random variables {X, Xn ; n ≥ 1} with weighted partial sums Sn (X, w ({dot operator})) = ∑k = 1n w (frac(k, n)) Xk, n ≥ 1 where w (t), 0 ≤ t ≤ 1 is a Lipschitz function of order 1 with {norm of matrix} w ({dot operator}) {norm of matrix}2 = sqrt(∫01 w2 (t) d t) > 0, necessary and sufficient conditions are provided for X to enjoy iterated logarithm type behavior of the form 0 < lim supn → ∞ | Sn (X, w ({dot operator})) | / sqrt(n h (n)) < ∞ almost surely where h ({dot operator}) is a positive, nondecreasing function which is slowly varying at infinity. Some corollaries are presented for particular choices of h ({dot operator}).

Original languageEnglish (US)
Pages (from-to)643-651
Number of pages9
JournalStatistics and Probability Letters
Volume79
Issue number5
DOIs
StatePublished - Mar 1 2009

Fingerprint Dive into the research topics of 'Iterated logarithm type behavior for weighted sums of i.i.d. random variables'. Together they form a unique fingerprint.

  • Cite this