Parameter Estimation
Equation (16.6) is useful for parameter estimation. Let
the mean depend on a set of mean parameters
,
and let the spectrum values
depend on
spectral parameters
. Let
the first derivatives of
be denoted by
We have

(16.7) 

(16.8) 
where
, and , are defined implicitly.
Using (16.7), the Fisher's information between spectral parameters and equals
Before carrying out the derivative with respect to , notice that
is zero in expected value. Therefore, the only terms remaining are
associated with the derivative of . Note that
Therefore,

(16.9) 
Using (16.8), for ``mean" parametrs,
Before carrying out the derivative with respect to , notice that
is zero in expected value. Therefore, the only terms remaining are
associated with the derivative of . Note that
Therefore,

(16.10) 
Baggenstoss
20170519