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Invariance of the Fisher matrix

  1. Dec 18, 2011 #1
    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?

  2. jcsd
  3. Dec 18, 2011 #2
    The Fisher information matrix is equivalent to the reciprocal of the asymptotic variance-covariance matrix of the parameter. Under the transformation [itex]T(\vec{x})=A(\vec{x})[/itex] the information content of the matrix is unchanged.

    Biometrika(1998)85,4 pp973-979
    Last edited: Dec 18, 2011
  4. Dec 19, 2011 #3
    great thanks!
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