On measuring internal dependence in a set of random variables
type: Item
instance of: scholarly article
title: On measuring internal dependence in a set of random variables
zbMATH Open document ID: 0631.62069
author: Robert A. Koyak
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: To measure dependence in a set of random variables, a multivariate analog of maximal correlation is considered. This consists of transforming each of the variables so that the largest partial sum of the eigenvalues of the resulting correlation matrix is maximized. A ``maximalized'' measure of association obtained in this manner permits statements to be made about the strength of internal dependence exhibited by the random variables. It is shown, under a weak regularity condition, that optimizing transformations exist and that they satisfy a geometrically interpretable fixed point property. If the variables are jointly Gaussian, then the identity transformation is shown to be optimal, which extends Kolmogorov's result for canonical correlation to the principal components setting.
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 4026595
zbMATH Keywords: maximal correlation
zbMATH Keywords: optimizing transformations
zbMATH Keywords: fixed point property
zbMATH Keywords: identity transformation
zbMATH Keywords: canonical correlation
zbMATH Keywords: principal components
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350501
OpenAlex ID: W2036039538
DOI: 10.1214/AOS/1176350501
description: scientific article; zbMATH DE number 4026595