An approach is presented to get interconnections between the Fisher information matrix of an ARMAX process and a corresponding
solution of a Stein equation. The case of algebraic multiplicity greater than one and the case of distinct eigenvalues are
addressed. Appropriate links are constructed for these two cases by applying a factorization both for the Fisher information
matrix and for a corresponding solution of a Stein equation. These factored forms are nonsquare linear systems of equations
Ax = b, the kernels of the appropriate coefficient matrices are described. These are of fundamental importance for the solutions
of the obtained linear systems. The structured coefficient matrix associated with the factored form of the Fisher information
matrix is composed by basis vectors associated with an ARMAX polynomial, whereas the coefficient matrix obtained through the
solution of a Stein equation consists of resolvant matrices associated with a companion matrix used in a corresponding Stein
equation. The presence of Vandermonde matrices in right inverses of coefficient matrices of the obtained linear systems is
investigated. Links between coefficient matrices which originate both from the Fisher information matrix and a corresponding
solution of the Stein equation are derived. An example is provided for illustrating a solution of a Stein equation in terms
of the Fisher information matrix as well as for describing the kernels of the appropriate coefficient matrices.

- Downloads

#### Disclaimer/Complaints regulations

If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.