Parametric and Nonparametric Models

Definition

A statistical model is a set of distributions (or densities or regression functions). A parametric model is a set that can be parameterized by a finite number of parameters.

Example

If we assume that the data come from a Normal distribution, then the model is

This is a two-parameter model.

We write the density as to show that is the value of the rando variable, whereas and are parameters.

Definition

In general, a parametric model takes the form

where is an unknown parameter (or vector of parameters) that can take values in the parameter space .

Sources

• Wasserman, L. (2010). All of Statistics: A concise Course in Statistical Inference. Chapter 6.2.