Application of a Frequency Domain Approach in Analysis of a Statistical Signal Estimator

In estimating a finite length signal vector that has been corrupted by additive stationary noise, a variety of statistical estimation forms exist. These forms may be based on least squares, maximum likelihood, empirical Bayes, or minimax principles. Often, the actions of such forms are not readily evident, in contrast to those of frequency domains forms used in engineering and based on an infinite time assumption. In this paper we demonstrate the use of a frequency domain approximation of a statistical signal estimator which belongs to a class of minimax forms. This approximation results in the discovery of a fundamental flaw common to that entire class of estimators. The simple form of the approximation also leads to an improved version which is, in an example, shown to perform better than the original estimator for a variety of noise processes. Finally, for the white noise situation, it is shown that the estimator, which becomes a classic, often used statistical form, is an empirical Wiener filter form which is so simple that it could be improved upon with minimal effort.