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 corre...

A necessary and suucient condition for equality in the matrix form of the Fisher-Information inequality is derived. In this technical report we consider the matrix form of the Fisher Information Inequality (FII), which was introduced in 5]. In particular, we provide a necessary and suucient condition for equality in the matrix-FII. We rst introduce a special form of Fisher Information (FI), cal...

We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are those of information geometry. The context is general enough to include applications from outside statistics.

We derive general expressions for the multi-tracer Fisher matrix, both assuming that cross-spectra are constrained by auto-spectra, and also allowing independent degrees of freedom in cross-spectra. show that, just like ratios power spectra, not cosmic variance. Moreover, whereas uncertainties spectra decrease with number density tracers as $\sim 1/\sqrt{\bar{n}}$, even faster, 1/\bar{n}$. simp...