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A New Parametrization of Correlation Matrices
Author(s) -
Archakov Ilya,
Hansen Peter Reinhard
Publication year - 2021
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta16910
Subject(s) - parametrization (atmospheric modeling) , generalization , covariance matrix , positive definiteness , matrix (chemical analysis) , mathematics , transformation (genetics) , transformation matrix , correlation , positive definite matrix , combinatorics , pure mathematics , algorithm , physics , mathematical analysis , materials science , eigenvalues and eigenvectors , quantum mechanics , chemistry , geometry , biochemistry , kinematics , gene , composite material , radiative transfer
We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z ‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector inR n ( n − 1 ) / 2is provided, and we derive its numerical complexity.