Criteria for parameters

Preliminaries

In some applications analysis and interpretation may be based on nonparametric formulations, for example the use of smooth curves or surfaces summarizing complex dependencies not easily captured in a simple formula. The reporting of estimated spectral densities of time series or line spectra representing complex mixtures of molecules are examples. Mostly, however, we aim to summarize the aspects of interest by parameters, preferably small in number and formally defined as properties of the probability model. In the cases on which we concentrate, the distribution specified by the model is determined by a finite number of such unknown parameters.

For a specific research question, parameters may be classified as parameters of interest, that is, directly addressing the questions of concern, or as nuisance parameters necessary to complete the statistical specification. Often the variation studied is a mixture of systematic and haphazard components, with attention focused on the former.