Approximate design-based variance of functions of covariance matrix | Zendy

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Approximate design-based variance of functions of covariance matrix

Author(s) -

Imbi Traat

Publication year - 2004

Publication title -

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.

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