Definitions

# Formation matrix

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

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 $j^\left\{ij\right\}$ 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.