Finite-memory algorithms for estimating the mean of a Gaussian distribution (Corresp.)
Martin E. Hellman · IEEE Transactions on Information Theory · 1974
Let\{X_n\}_{n=1}^{\infty}be independent random variables, each having a\mathcal{N}(\mu, \sigma^2)distribution. If we try to estimate\muwith anm-state learning algorithm, then the minimum mean-squared error is bounded below by that obtained by the bestm-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\thetaof a uniform distribution.