Local Weighting |
The size of the local neighborhoods that PROC LOESS uses in performing local fitting is determined by the smoothing parameter value . When
, the local neighborhood used at a point
contains the
fraction of the data points closest to the point
. When
, all data points are used.
Suppose denotes the number of points in the local neighborhoods and
denote the distances in increasing order of the
points closest to
. The point at distance
from
is given a weight
in the local regression that decreases as the distance from
increases. PROC LOESS uses a tricube weight function to define
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If , then
is replaced by
in the previous formula, where
is the number of predictors in the model.
Finally, note that if a weight variable has been specified using a WEIGHT statement, then is multiplied by the corresponding value of the specified weight variable.