We present a method to simplify the analytical computation of the Cram
er-Rao bound. The method circumvents bound calculations for so-called
nuisance parameters. Under mild regularity conditions the technique, w
hich replaces expectations with almost sure limits, can significantly
lower the analytical complexity as compared to traditional methods. Th
e dimension of a matrix that requires computation and inversion is red
uced to the length of the parameter vector of interest. We give applic
ations to random variables having densities in the exponential family.
For normal distributions the resulting expressions take on particular
ly simple closed forms.