### Nonparametric Regression

Subsections:

Parametric regression models express the mean of an observation as a function of the regressor variables and the parameters :

Not only do nonparametric regression techniques relax the assumption of linearity in the regression parameters, but they also do not require that you specify a precise functional form for the relationship between response and regressor variables. Consider a regression problem in which the relationship between response Y and regressor X is to be modeled. It is assumed that , where is an unspecified regression function. Two primary approaches in nonparametric regression modeling are as follows:

• Approximate locally by a parametric function that is constructed from information in a local neighborhood of .

• Approximate the unknown function by a smooth, flexible function and determine the necessary smoothness and continuity properties from the data.

The SAS/STAT procedures ADAPTIVEREG, LOESS, TPSPLINE, and GAM fit nonparametric regression models by one of these methods.