Local Weighting

The LOESS Procedure

Local Weighting

The size of the local neighborhoods that PROC LOESS uses in performing local fitting is determined by the smoothing parameter s. When s < 1, the local neighborhood used at a point x contains the s fraction of the data points closest to the point x. When $s \geq 1$ , all data points are used.

Suppose q denotes the number of points in the local neighborhoods and d₁,d₂, ... ,d_q denote the distances in increasing order of the q points closest to x. The point at distance d_i from x is given a weight w_i in the local regression that decreases as the distance from x increases. PROC LOESS uses a tricube weight function to define

w_i = [32/5] (1-([(d_i)/(d_q)])³ )³

If s>1, then d_q is replaced by d_q s^1/p in the previous formula, where p is the number of predictors in the model.

Finally, note that if a weight variable has been specified using a WEIGHT statement, then w_i is multiplied by the corresponding value of the specified weight variable.

Chapter Contents
Previous
Next
Top