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Bounds on the Bayes and minimax risk for signal parameter estimation

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2 Author(s)
L. D. Brown ; Dept. of Math., Cornell Univ., Ithaca, NY, USA ; R. C. Liu

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

Published in:

IEEE Transactions on Information Theory  (Volume:39 ,  Issue: 4 )