![]() | This article may be too technical for most readers to understand.(May 2014) |
In statistics and information theory, the expected formation matrix of a likelihood function is the matrix inverse of the Fisher information matrix of , while the observed formation matrix of is the inverse of the observed information matrix of . [1]
Currently, no notation for dealing with formation matrices is widely used, but in books and articles by Ole E. Barndorff-Nielsen and Peter McCullagh, the symbol is used to denote the element of the i-th line and j-th column of the observed formation matrix. The geometric interpretation of the Fisher information matrix (metric) leads to a notation of following the notation of the ( contravariant) metric tensor in differential geometry. The Fisher information metric is denoted by so that using Einstein notation we have .
These matrices appear naturally in the asymptotic expansion of the distribution of many statistics related to the likelihood ratio.
![]() | This article may be too technical for most readers to understand.(May 2014) |
In statistics and information theory, the expected formation matrix of a likelihood function is the matrix inverse of the Fisher information matrix of , while the observed formation matrix of is the inverse of the observed information matrix of . [1]
Currently, no notation for dealing with formation matrices is widely used, but in books and articles by Ole E. Barndorff-Nielsen and Peter McCullagh, the symbol is used to denote the element of the i-th line and j-th column of the observed formation matrix. The geometric interpretation of the Fisher information matrix (metric) leads to a notation of following the notation of the ( contravariant) metric tensor in differential geometry. The Fisher information metric is denoted by so that using Einstein notation we have .
These matrices appear naturally in the asymptotic expansion of the distribution of many statistics related to the likelihood ratio.