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INDEPENDENCE DISTRIBUTION‐PRESERVING NONNEGATIVE‐DEFINITE COVARIANCE STRUCTURES FOR THE SAMPLE VARIANCE
Author(s) -
Young Dean M.,
Lehman Leah M.,
Meaux Laurie M.
Publication year - 1996
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1996.tb00675.x
Subject(s) - univariate , covariance , law of total covariance , mathematics , multivariate normal distribution , covariance matrix , independent and identically distributed random variables , statistics , variance (accounting) , sample (material) , independence (probability theory) , estimation of covariance matrices , sample mean and sample covariance , positive definite matrix , sample variance , multivariate statistics , random variable , covariance intersection , chemistry , eigenvalues and eigenvectors , accounting , physics , chromatography , quantum mechanics , estimator , business
Summary This paper explicitly characterizes the general nonnegative‐definite covariance structure for a multivariate normal random vector such that the univariate sample variance is distributed exactly as if the sample observations are normal independent and identically distributed (i.i.d.). This work extends the results of Baldessari (1965) and Stadje (1984) who have characterized the general positive‐definite covariance matrix such that the univariate sample variance is distributed exactly as if the sample observations are normal i.i.d.