A bound on mean square estimate error

A lower bound on mean square estimate error is derived as an instance of the covariance inequality by concatenating the generating matrices for the Bhattacharyya and Barankin bounds; it represents a generalization of the Bhattacharyya (1946), Barankin (1949), Cramer-Rao (1945), Hammersley-Chapman-Robbins (1950, 1951), Kiefer (1952), and McAulay-Hofstetter (1971) bounds in that all of these bounds can be derived as special cases. The bound is applicable to biased estimates of vector-valued functions of a vector-valued parameter. Termed the hybrid Bhattacharrya-Barankin bound, it can be written as the sum of the mth-order Bhattacharrya bound and a nonnegative correction term dependent on a set of r so-called test points. It is intended for use when small-error bounds, such as the Cramer-Rao bound, may not be tight; unlike many large-error bounds, it is relatively easy to compute while providing a smooth transition between the small- and large-error regions.<>