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On a relation between detection and estimation in decision theory. (English) Zbl 0165.22203

Summary: It is shown that in the estimation of an arbitrary signal corrupted by additive Gaussian noise, the optimum minimum-variance estimator is always a simple linear transformation of the logarithmic gradient of the average likelihood ratio which is obtained in the optimum detection of the same signal. Conversely, the average likelihood ratio can always be expressed in a simple functional form containing only the minimum-variance estimator of the unknown signal.

MSC:

94A13 Detection theory in information and communication theory
62C99 Statistical decision theory
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