### 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 2017-05-19