Statistical meaning of Carlen's superadditivity of the Fisher information

✍ Scribed by Abram Kagan; Zinoviy Landsman

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 166 KB
• Volume: 32
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00070-3

✦ Synopsis

In Carlen (1991) a property of the Fisher information called "superadditivity", was proved via analytic means. We show that the superaddifivity is a corollary of the following simple statistical principle which is of an independent interest. The Fisher information about a parameter 0 contained in an observation X = (Y,Z) with a density f(y -O,z) is never less than the Fisher information in the first component Y with the equality iff Y is independent of Z.