Degree-one Models and Cross Product Matrices

Degree-one models can be applied to cross products matrices and Hilbert-Schmidt scalar products matrices. The latter have an important role in the first stage (inter-structure) of STATIS methodology, while the former matrices (in particular the AAt and AtA cross products, which have the same non-null eigenvalues) have an important role in inference. The case of rank one is interesting since the first eigenvector of matrix XXt may be used to describe the behavior of the variables corresponding to the columns of X. We now consider the estimators of the pair (λ, α) and testing that the mean matrix as rank one. We apply our results to cross product matrices XXt, given an numerical example