On the strong law for arrays and for the bootstrap mean and variance
type: Item
instance of: scholarly article
title: On the strong law for arrays and for the bootstrap mean and variance
zbMATH Open document ID: 0883.60024
DOI: 10.1155/S0161171297000483
author: Tienchung Hu
author: Robert L. Taylor
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1998-02-23T00:00:00Z
full work available at URL: https://eudml.org/doc/47832
review text: The strong law of large numbers for a triangular array \(\{X_{ni}\), \(1\leq i \leq n, n\geq 1\}\) of row-wise independent (but neither necessarily identically distributed nor independent between rows) random variables is established under conditions similar to those of Chung. Further this result is related to verifying a known fact of consistency of the bootstrap mean and bootstrap variance [cf. \textit{S. C\"sorgö}, Stat. Probab. Lett. 14, No. 1, 1-7 (1992; Zbl 0752.62034)]. The authors present a new, fairly different approach to this problem in a natural formulation. Let us mention that in Theorem 2.1 not only a.s. but even complete convergence can be stated.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60B12
zbMATH DE Number: 1046346
zbMATH Keywords: strong law of large numbers
zbMATH Keywords: row-wise independent
zbMATH Keywords: triangular arrays
zbMATH Keywords: bootstrap mean and variance
zbMATH Keywords: Chung's strong law of large numbers
reviewed by: Andrei Volodin
MaRDI profile type: Publication
OpenAlex ID: W2090878544
description: scientific article; zbMATH DE number 1046346