An Algorithm to Improve and Validate Cramer-Rao Bounds Through the Fibre Bundle Theory of Local Exponential Families

An algorithm is proposed that can be used (i) to verify the validity of the asymptotic Cramer-Rao bound (CRB) for a finite number of observations; (ii) to improve the CRB. It is derived from the fibre bundle theory of local exponential families developed by Amari and by Barndorff-Nielsen et al. The algorithm is applicable to any regular estimation problem. As an illustration, the problem of estimating the parameters of an AR model with noisy observations is considered.