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Fisher's information

The Fisher's information is given by

$\displaystyle I_{{\bf a}{\bf a}} = \frac{1}{\sigma^2} {\bf H}^{\prime}_\theta {... ...}^\theta_\theta {\bf a}, \;\;\;\;\; I_{\sigma^2\sigma^2} = \frac{N}{2\sigma^4}.$

These cross-terms are zero:

$\displaystyle I_{{\bf a}\sigma^2}=I_{\theta\sigma^2}=0.$