In Carlen (1991) a property of the Fisher information called "superadditivity", was proved via analytic means. We show that the superadditivity is a corollary of the following simple statistical principle which is of an independent interest. The Fisher information about a parameter θ contained in an observation X = (Y,Z) with a density f(y - θ,z) is never less than the Fisher information in the first component Y with the equality iff Y is independent of Z.
- Fisher information
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty