Invariance of the Fisher matrix

1. Dec 18, 2011

lukluk

Fisher matrix=(minus the) average of the second derivative of the log-likelihood with respect to the parameters

It seems to me the Fisher matrix for Gaussian data is invariant with respect to any (non-singular) linear transformation of the data; if correct this is a very useful property, however I cannot find a reference to this in the texts available to me. Can anyone confirm whether this is true or refer me to some discussion of this?

Thanks!

2. Dec 18, 2011

SW VandeCarr

The Fisher information matrix is equivalent to the reciprocal of the asymptotic variance-covariance matrix of the parameter. Under the transformation $T(\vec{x})=A(\vec{x})$ the information content of the matrix is unchanged.

Biometrika(1998)85,4 pp973-979

Last edited: Dec 18, 2011
3. Dec 19, 2011

lukluk

great thanks!