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I want to understand how minimizing the determinant of the information matrix is equivalent to maximizing the differential Shannon entropy? A similar question was posted in Math SE but hasnt been rigorously answered.

My understanding is that, by minimizing the determinant of information matrix we are trying to minimize the deviation of our estimator from the true distribution because ideally a 0 determinant implies singularity or the 0 deviation of the estimator from the actual distribution.

The question is: How does this relate to maximizing differential Shannon entropy? How are we maximizing information?

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