The estimation theory deals with the basic problem of infering some relevant features of a random experiment based on the observation of the experiment outcomes. In some cases, the experiment mechanism is totally unknown to the observer and the use of nonparametric estimation methods is necessary. The term “nonparametric” means that the observed experiment cannot be modelled mathematically. Let us consider, for instance, the classical problem of spectral analysis that consists in computing the power spectral density of the observed signal from a finite sample. The performance of nonparametric methods is usually unsatisfactory when the observed time is limited. This situation is actually very usual because the experiment output is only temporally available; the experiment is not stationary; or the observer is due to supply the estimate in a short time. To design more efficient estimation techniques, it is recommended to find previously a convenient mathematical model for the studied experiment. The result of the experiment is thus a function of a finite number of unknow parameters, say θ, and other random terms forming the vector w. The vector w collects all the nuisance terms in the model that vary randomly during the observation time as, for example, the measurement noise.

The objective is therefore finding the minimal parameterization in order to concentrate the most the uncertainty about the experiment. In those fields dealing with natural phenomena, the parametrization of the problem is definitely the most difficult point and, actually, the ultimate goal of scientists working in physics, sociology, economics, among others. Fortunately, the parameterization of human-made systems is normally accesible. In particular, in communication engineering, the received signal is known except for a finite set of parameters that must be estimated before recovering the transmitted information. Likewise, in radar applications, the received signal is know except for the time of arrival and, possibly, some other nuisance parameters. In the following, we will focus exclusively on parametric estimation methods assuming that we are provided with a convenient parameterization or signal model.

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Adam Smith,
Editorial Manager,
Research Journal of Economics