Concentrated Cramer-Rao bound expressions

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