An Alternative Proof For the Minimum Fisher Information of Gaussian Distribution

• Main Author: Pak Abbas
• Format: Article
• Language: English
• Published: Sciendo 2018-12-01
• Series: Journal of Applied Mathematics, Statistics and Informatics
• Subjects: 62H12; 62H10; 62F12; Fisher information; Gaussian distribution; Minimum risk equivariant estimator
• Online Access: http://www.degruyter.com/view/j/jamsi.2018.14.issue-2/jamsi-2018-0008/jamsi-2018-0008.xml?format=INT

Fisher information is of key importance in estimation theory. It is used as a tool for characterizing complex signals or systems, with applications, e.g. in biology, geophysics and signal processing. The problem of minimizing Fisher information in a set of distributions has been studied by many researchers. In this paper, based on some rather simple statistical reasoning, we provide an alternative proof for the fact that Gaussian distribution with finite variance minimizes the Fisher information over all distributions with the same variance.