Decomposition of the observation vector in estimation of covariance matrices of special structure

The paper is concerned with estimation of the covariance matrix of an observed random vector value. It is assumed that the unknown covariance matrix belongs to a certain symmetrical algebra. The structure of the algebra's matrices is used for decomposition of the observation vector and for reducing the estimation poblem to simpler statistical problems. Unbiased and optimal invariant estimates are obtained for covariance matrices.