The LOESS Procedure

Smoothing Matrix

When no iterative reweighting is done, the "Smoothing Matrix" denoted by $\bL $ defines the linear relationship between the fitted and observed dependent variable values of a loess model. You can obtain the predicted values of a loess fit from the observed values via

\[ \hat{\mb{y}}=\bL \mb{y} \]

where $\mb{y}$ is the vector of observed values and $\hat{\mb{y}}$ is the corresponding vector of predicted values of the dependent variable. Note that $\bL $ is an n by n matrix, where n is the number of observations in the analysis. PROC LOESS does not explicitly form $\bL $ if the DFMETHOD=EXACT option is not explicitly or implicitly selected.