Bounds on the Bayes and minimax risk for signal parameter estimation

In estimating the parameter θ from a parametrized signal problem (with 0⩽θ⩽L) observed through Gaussian white noise, four useful and computable lower bounds for the Bayes risk are developed. For problems with different L and different signal to noise ratios, some bounds are superior to 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 is shown in the lower bound