On the weak law of large numbers for arrays
type: Item
instance of: scholarly article
title: On the weak law of large numbers for arrays
zbMATH Open document ID: 0815.60023
DOI: 10.1016/0167-7152(94)00047-C
author: Dug Hun Hong
author: Kwang Sik Oh
published in: Statistics \& Probability Letters
publication date: 1995-02-22T00:00:00Z
review text: A weak law of large numbers is proved for an array \(X_{ni}\), \(1 \leq i \leq k_ n\), \(n \geq 1\), \(k_ n \to \infty\), under the assumption that for some \(p \in (0,2)\), \[ \lim_{a \to \infty} {1\over k_ n} \sum^{k_ n}_{i = 1} aP(| X_{ni}| > a) = 0 \text{ uniformly in }n. \] Compare \textit{A. Gut's} result [ibid. 14, No. 1, 49-52 (1992; Zbl 0769.60034)] who obtained \(L^ p\)-convergence on a somewhat stronger domination condition.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 724094
zbMATH Keywords: arrays
zbMATH Keywords: weak law of large numbers
zbMATH Keywords: domination condition
reviewed by: Heinrich Hering
MaRDI profile type: Publication
cites work: Q4606219
cites work: Q5753278
cites work: An $L^p$-Convergence Theorem
cites work: On the $L_p$-Convergence for $n^{-1/p} S_n, 0 &lt; p &lt; 2^1$
cites work: Q4040465
cites work: On convergence in r-mean of some first passage times and randomly indexed partial sums
cites work: The weak law of large numbers for arrays
cites work: On the Lp convergence of sums of independent random variables
cites work: On Convergence in $r$-Mean of Normalized Partial Sums
cites work: A limit theorem for double arrays
description: scientific article; zbMATH DE number 724094