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- W2185708237 abstract "The Cramer-Rao bound establishes the lower limit on how much “information” about an unknown probability distribution parameter a set of measurements carries. More specifically, the inequality establishes the minimum variance for an unbiased estimator of the underlying parameter, θ, of a probability distribution, p(x; θ). Three important points must be kept in mind about the CramerRao bound: 1) the bound pertains only to unbiased estimators, biased estimators may violate the lower bound 2) the bound may be unreachable in practice, and 3) maximum likelihood estimators achieve the lower bound as the size of the measurement set tends to infinity. The following note outlines the proof of the Cramer-Rao bound for a single parameter (adapted from (Gershenfeld, 1999)). Before proving the Cramer-Rao bound, let’s first establish several key components of the proof. The score, S is defined as," @default.
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- W2185708237 title "Cramer-Rao Bound" @default.
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