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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Relation between multivariate estimation error and differential entropy
On page 255 of the book "Elements of information theory" by Thomas M. Cover and Joy A. Thomas, there is a theorem: For any random variable $X$ and estimator $\hat{X}$, $$E(X-\hat{X})^2 \geq \min_{\hat …