Bounds on the Bayes and minimax risk for signal parameter estimation

A 3 r m h estimating the parameter 0 from a parametrized signal problem (with 0 5 0 5 L) observed through Gaussian white noise, four useful and computable lower bounds for the Bayes risk were developed. For problems with different L and Merent signal to noise ratios, some bounds am superior to the others. The lower bound obtained from taking the maximum of the four, serves not only as a good lower bound for the Bayes risk but also as a good lower bound for the minimax risks. Threshold behavior of the Bayes risk is also evident as shown in our lower bound.