Open AccessApproximate design-based variance of functions of covariance matrix
Author(s) -
Imbi Traat
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.2004.08.22
Subject(s) - mathematics , estimator , covariance matrix , independent and identically distributed random variables , series (stratigraphy) , taylor series , variance (accounting) , law of total covariance , matrix (chemical analysis) , covariance , population , statistics , estimation of covariance matrices , covariance intersection , random variable , mathematical analysis , paleontology , materials science , demography , accounting , composite material , sociology , business , biology
Functions of a design-weighted estimator ^ S of the finite population covariance matrix are considered. For these functions (determinant, Hotelling’s T2) the approximate (Taylor series based) variances are derived. For ^ S also the exact dispersion matrix is derived. These are generalizations of earlier results for independent identically distributed (i.i.d.) variables. A simulation study supports the derived formulae.