In statistics and information theory, the expected formation matrix of a likelihood function L(\theta) is the matrix inverse of the Fisher information matrix of L(\theta), while the observed formation matrix of L(\theta) is the inverse of the observed information matrix of L(\theta).

Currently, no notation for dealing with formation matrices is widely used, but in Ole E. Barndorff-Nielsen and Peter McCullagh books and articles the symbol j^{ij} is used to denote the element of the i-th line and j-th column of the observed formation matrix.

These matrices appear naturally in the asymptotic expansion of the distribution of many statistics related to the likelihood ratio.

References

• Barndorff--Nielsen, O. and D.R. Cox, (1989), Asymptotic Techniques for Use in Statistics, Chapman and Hall, London.
• Barndorff-Nielsen, O.E. and Cox, D.R., (1994). Inference and Asymptotics. Chapman & Hall, London.
• P. McCullagh, "Tensor Methods in Statistics", Monographs on Statistics and Applied Probability, Chapman and Hall, 1987.

See also

• Fisher information
• Shannon entropy