Nonparametric and parametric models

The exact role of nonlinear methods in statistics is perhaps still a bit contentious. They are largely used for the purposes of exploratory analyses as visual tools, and for this reason data visualization and nonlinear statistical methods are closely tied together. The question is whether or not nonlinear methods can also be used to truly develop statistical models.

Broadly speaking, nonlinear models might be grouped into nonparametric (or semi-parametric) and parametric models. The term "parametric" here has a very different meaning than it does in statistical methods, used in testing for differences between groups. Parametric tests of statistically significant differences are concerned with a parameterization of the sample distribution. For example, the t-test does not actually test for differences in observed data but tests for differences in distributions whose parameters were computed based on observed data. This is to say, that we only need to know...