A nonuniform bound to an independent test in high dimensional data analysis via Stein's method
type: Item
instance of: scholarly article
title: A nonuniform bound to an independent test in high dimensional data analysis via Stein's method
zbMATH Open document ID: 1431.62240
DOI: 10.1155/2019/8641870
author: Nahathai Rerkruthairat
published in: Journal of Probability and Statistics
publication date: 2019-03-21T00:00:00Z
review text: Summary: The Berry-Esseen bound for the random variable based on the sum of squared sample correlation coefficients and used to test the complete independence in high diemensions is shown by Stein's method. Although the Berry-Esseen bound can be applied to all real numbers in \(\mathbb{R}\), a nonuniform bound at a real number \(z\) usually provides a sharper bound if \(z\) is fixed. In this paper, we present the first version of a nonuniform bound on a normal approximation for this random variable with an optimal rate of \(\left(1 / \left(0.5 + | z |\right)\right) \cdot O \left(1 / \sqrt{m}\right)\) by using Stein's method.
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 7039897
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/8641870
OpenAlex ID: W2913001347
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Wikidata QID: Q128494053
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description: scientific article; zbMATH DE number 7039897