Approximate design-based variance of functions of covariance matrix

Abstract

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.