CR Bound (FIM)

To apply (2.27), we need the FIM or the CR bound covariance (inverse of FIM). The CR bound for AR parameters is well known [25]. We have

$\displaystyle {\bf C}_{\bf a} = \frac{N}{\sigma^2}{\bf R},$

where $ {\bf R}$ is the $ P\times P$ auto-correlation matrix. Note that $ \frac{1}{\sigma^2}{\bf R}$ has asymptotically determinant 1.

The CR bound for $ \sigma^2$ is independent of $ {\bf C}_a$ and given by

$\displaystyle {\bf C}_{\sigma^2}=\frac{2\sigma^4}{N}.$

The function software/module_ar_ml.m implements this. We compare this method with other approaches in Section 9.4.10.

Baggenstoss 2017-05-19