Cramer-Rao bounds for AR parameter and reflection coefficient estimators

The finite examples Cramer-Rao bound for the autoregressive parameters of a Gaussian autoregressive model is given in closed form. Quick algorithms for computing this bound for the autoregressive parameters and also for the reflection coefficients are presented. The exact bounds are of interest since they can differ appreciably from the asymptotic bounds. If replicated independent records are available (as in some spatial array processing problems), the exact bounds will be approached when the number of replications goes to infinity but the asymptotic bound will not, since the record length remains finite