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:

$\displaystyle  \mbox{DF1}  $
$\displaystyle  \equiv  $
$\displaystyle  \mbox{Trace} (\bL )  $
$\displaystyle \mbox{DF2}  $
$\displaystyle  \equiv  $
$\displaystyle  \mbox{Trace} (\bL ^\prime \bL ) $
$\displaystyle \mbox{DF3}  $
$\displaystyle  \equiv  $
$\displaystyle  2 \mbox{Trace} \bL - \mbox{Trace} (\bL ^\prime \bL )  $

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.