Consideration of round off errors in the design of mean square estimators

In this correspondence, a search for the optimal polynomial mean-square (ms) estimator is undertaken; when the input is a vector with fixed dimensionality and at the calculation of the estimator characteristics the round off errors are considered. It is found that the accumulation of these errors causes divergence of the estimate from the theoretically ideal one. Also, the minimum mean-square error, instead of monotonically decreasing with the degree of the polynomial estimator, increases when This degree exceeds a number that depends on the statistics of the problem. This error is found to be equal to the sum of the ideal error e
0
and a term e
e
which includes the computational errors and increases monotonically with the degree of the estimator.