Formation matrix

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.E., Cox, D.R. (1989), Asymptotic Techniques for Use in Statistics, Chapman and Hall, London. ISBN 0-412-31400-2
• Barndorff-Nielsen, O.E., 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