A RECURSIVE ALGORITHM FOR COMPUTING CRAMER-RAO-TYPE BOUNDS ON ESTIMATOR COVARIANCE

We give a recursive algorithm to calculate submatrices of the Cramer-R ao (CR) matrix bound on the covariance of any unbiased estimator of a vector parameter theta. Our algorithm computes a sequence of lower bou nds that converges monotonically to the CR bound with exponential spee d of convergence. The recursive algorithm uses an invertible ''splitti ng 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 simila r to that of the well-known EM parameter estimation algorithm. As a co ncrete illustration we consider image reconstruction from projections for emission computed tomography.