On Problems of Estimation with Limited Resources

Some lower bounds on the mean-square estimation quality are given for independent observations with constraints on the number of operations $m$ the the observer (the “statistician”) can use to extract information from observations and on the number of possible values of the statistic $L$. These bounds depend on the combined action of two factors: the finite nature of the number of observations and the necessity of considering a quantized sample. It is shown that, under the given conditions, these bounds are asymptotically attainable.