A recursive algorithm for computing Cramer-Rao-type bounds on estimator covariance

We give a recursive algorithm to calculate submatrices of the Cramer-Rao (CR) matrix bound on the covariance of any unbiased estimator of a vector parameter θ_. Our algorithm computes a sequence of lower bounds that converges monotonically to the CR bound with exponential speed of convergence. The recursive algorithm uses an invertible “splitting matrix” to successively approximate the inverse Fisher information matrix. We present a statistical approach to selecting the splitting matrix based on a “complete-data-incomplete-data” formulation similar to that of the well-known EM parameter estimation algorithm. As a concrete illustration we consider image reconstruction from projections for emission computed tomography