Esposito, R. On a relation between detection and estimation in decision theory. (English) Zbl 0165.22203 Inf. Control 12, 116-120 (1968). 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. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 94A13 Detection theory in information and communication theory 62C99 Statistical decision theory Keywords:signal corrupted by additive Gaussian noise; average likelihood ratio; minimum-variance estimator; optimum detection PDFBibTeX XMLCite \textit{R. Esposito}, Inf. Control 12, 116--120 (1968; Zbl 0165.22203) Full Text: DOI