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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 amathcal{N}(mu, sigma^2)distribution. If we try to estimatemuwith anm-state learning algorithm, then the minimum mean-squared error is bounded below by that obtained by the bestm-level quantizer (which requires knowledge ofmu). Here we show that this lower bound is tight. The results are easily extended to a number of other problems, such as estimating the meanthetaof a uniform distribution.

Published in:

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

Date of Publication:

May 1974

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