Parametric vs. non-parametric models

在查 non-parametric tests 时，Wikipedia 上提到了 Non-parametric models，于是干脆就记录一下。参考 Wikipedia: Parametric model。

---

In statistics, a parametric model or parametric family or finite-dimensional model is a family of distributions that can be described using a finite number of parameters. These parameters are usually collected together to form a single $ k $-dimensional parameter vector $ \theta = (\theta_1, \theta_2, \cdots, \theta_k) $.

Parametric models are contrasted with the semi-parametric, semi-nonparametric, and non-parametric models, all of which consist of an infinite set of “parameters” for description. The distinction between these four classes is as follows:

• a model is “parametric” if all the parameters are in finite-dimensional parameter spaces;
• a model is “non-parametric” if all the parameters are in infinite-dimensional parameter spaces;
• a “semi-parametric” model contains finite-dimensional parameters of interest and infinite-dimensional nuisance ([ˈnju:sns], something annoying) parameters;
• a “semi-nonparametric” model contains finite-dimensional and infinite-dimensional unknown parameters of interest.

常见的 non-parametric model 比如：KNN, SVM, splines.