How to transform correlated random variables into uncorrelated ones
type: Item
instance of: scholarly article
title: How to transform correlated random variables into uncorrelated ones
zbMATH Open document ID: 0954.62074
DOI: 10.1016/S0893-9659(00)00050-1
published in: Applied Mathematics Letters
publication date: 2000-11-16T00:00:00Z
review text: For an arbitrary random vector \({\mathbf X}= (X_1,X_2, \dots, X_n)\), we can always construct uncorrelated random variables \(Y_1,Y_2, \dots, Y_n\) and \((R\to R)\) functions \(f_1,f_2, \dots,f_n\), such that \[ (X_1, X_2, \dots, X_n)= (f_1(Y_1),f_2(Y_2), \dots, f_n(Y_n)). \] Although the \(f\) s cannot always be one-to-one, in many important cases, the \(f\) s are not only one-to-one but also piecewise linear, e.g. if \({\mathbf X}\) is normally distributed. (This way, in many statistical models, the nuisance parameters can easily be transformed, such that their MLEs become uncorrelated with other parameters).
Mathematics Subject Classification ID: 62H20
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 62H05
zbMATH DE Number: 1531197
zbMATH Keywords: reparametrization
zbMATH Keywords: one-to-one transformations
zbMATH Keywords: monotone functions
zbMATH Keywords: covariance
author: Arjun K. Gupta
author: Tamás F. Móri
author: G. J. Székely
MaRDI profile type: Publication
cites work: Q5794069
cites work: Q4725475
cites work: Essential correlatedness and almost independence
cites work: Some Concepts of Dependence
cites work: Q5778074
full work available at URL: s0893-9659(00)00050-1
OpenAlex ID: W2029914080
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description: scientific article; zbMATH DE number 1531197