Empirical correlation operator and many-dimensional Hermite polynomials
type: Item
instance of: scholarly article
title: Empirical correlation operator and many-dimensional Hermite polynomials
zbMATH Open document ID: 0812.60012
DOI: 10.1007/BF01061448
author: V. I. Stepakhno
published in: Ukrainian Mathematical Journal
publication date: 1994-11-10T00:00:00Z
review text: This paper deals with an operator, which the author calls an empirical correlation operator, operating on the subspace of vector Hermite polynomials of a given order. The asymptotic properties of this operator are studied by considering a simple random sample of size \(n\) from an \(m\)-variate Gaussian population. The results obtained in this paper extend earlier results on the asymptotic behaviour of the spectrum of the operator when \(n\) and \(m\) go to infinity with \(m/n\) going to a finite quantity.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C50
Mathematics Subject Classification ID: 62H99
zbMATH DE Number: 652264
zbMATH Keywords: multivariate Hermite polynomials
zbMATH Keywords: correlation operator
zbMATH Keywords: projection operator
zbMATH Keywords: vector Hermite polynomials
zbMATH Keywords: asymptotic properties
reviewed by: Arakaparampil M. Mathai
MaRDI profile type: Publication
cites work: On the limit of the largest eigenvalue of the large dimensional sample covariance matrix
cites work: Q3707099
cites work: Generalization of Hermite polynomials
cites work: A central limit theorem for Hermitian polynomials of independent Gaussian variables
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description: scientific article; zbMATH DE number 652264