Open AccessDensity expansions for correlations and eigenvalues of the covariance matrix
Author(s) -
Tõnu Kollo,
Anne Selart
Publication year - 2004
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2004.08.11
Subject(s) - univariate , mathematics , covariance matrix , eigenvalues and eigenvectors , sample mean and sample covariance , covariance , multivariate statistics , multivariate normal distribution , skew , matrix (chemical analysis) , estimation of covariance matrices , statistics , skew normal distribution , sample (material) , normal distribution , physics , chemistry , quantum mechanics , estimator , astronomy , thermodynamics , chromatography
In the paper explicit approximation formulae for the sample correlation coefficient and eigenvalues of the sample covariance matrix are found. The approximations are based on univariate and multivariate normal and skew normal distributions. A simulation experiment has been carried out where the empirical distributions are compared with different approximations.