Invariance of the Fisher matrix

[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!

 

[SW VandeCarr]

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!

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

 

[lukluk]

great thanks!