A model for robust analysis of multivariate data (Q1061426)

The author considers the model \(U=\mu +SV\), where \(\mu\) is an (m\(\times 1)\) vector of constants, S is an (m\(\times m)\) matrix of constants, U is the (m\(\times 1)\) vector of independent observations and the elements of the (m\(\times 1)\) vector V are assumed to be iid rv's of continuous type with zero location and unit scale. In the first part maximum likelihood estimators of \(\mu\) and S are derived in detail, a class of M-estimators of \(\mu\) and S is suggested and the theory is illustrated for the case of normally distributed vectors V. In the second part the author shows how principal components based on the model are to be constructed.