Invariance of the Fisher matrix

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The Fisher matrix for Gaussian data is invariant under any non-singular linear transformation, which is a significant property for statistical analysis. This invariance implies that the information content of the matrix remains unchanged despite transformations. The Fisher information matrix is also equivalent to the reciprocal of the asymptotic variance-covariance matrix of the parameters. A reference to this property can be found in Biometrika (1998) 85,4 pp973-979. Understanding this invariance can enhance the application of the Fisher matrix in various statistical contexts.
lukluk
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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!
 
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lukluk said:
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
 
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great thanks!
 
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