Estimation of a covariance matrix with location: Asymptotic formulas and optimal B-robust estimators

Applying the non-singular affine transformations AZ + [mu] to a spherically symmetrically distributed variate Z generates the covariance-location model, indexed by the parameters AAT and [mu], consisting of so-called elliptical distributions. We develop an algebraic machinery that simplifies the derivation of influence functions and asymptotic variance-covariance matrices for equivariant estimators of [Sigma] and [mu] and reveals a natural structure of [Sigma]. In addition, optimal B-robust estimators are derived.