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Finite-memory algorithms for estimating the mean of a Gaussian distribution (Corresp.)

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Let {X_n}_{n=1}^{\infty } be independent random variables, each having a mathcal{N}(\mu, \sigma ^2) distribution. If we try to estimate \mu with an m -state learning algorithm, then the minimum mean-squared error is bounded below by that obtained by the best m -level quantizer (which requires knowledge of \mu ). Here we show that this lower bound is tight. The results are easily extended to a number of other problems, such as estimating the mean \theta of a uniform distribution.

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IEEE Transactions on Information Theory  (Volume:20 ,  Issue: 3 )