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

AbstractApplying the non-singular affine transformations AZ + μ to a spherically symmetrically distributed variate Z generates the covariance-location model, indexed by the parameters AAT and μ, 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 Σ and μ and reveals a natural structure of Σ. In addition, optimal B-robust estimators are derived