The LOESS Procedure

Model Degrees of Freedom

The approximate model degrees of freedom in a nonparametric fit is a number that is analogous to the number of free parameters in a parametric model. There are three commonly used measures of model degrees of freedom in nonparametric models. These criteria are as follows:

StartLayout 1st Row 1st Column DF 1 2nd Column identical-to 3rd Column Trace left-parenthesis bold upper L right-parenthesis 2nd Row 1st Column DF 2 2nd Column identical-to 3rd Column Trace left-parenthesis bold upper L prime bold upper L right-parenthesis 3rd Row 1st Column DF 3 2nd Column identical-to 3rd Column 2 Trace bold upper L minus Trace left-parenthesis bold upper L prime bold upper L right-parenthesis EndLayout

A discussion of their properties can be found in Hastie and Tibshirani (1990). DF2 is also referred to as the "Equivalent Number of Parameters," and this is the name that PROC LOESS uses for DF2 when it appears in the "Fit Summary" table.

Last updated: December 09, 2022