Locally Weighted Linear Regression in LOWESS: Cleveland’s Method
Lowess (locally weighted scatterplot smoothing) is a robust weighted regression smoothing algorithm introduced by William S. Cleveland in 1979. Cleveland also made available FORTRAN routines LOWESS and LOWEST from the Computing Information Library at Bell Laboratories. These are reproduced in the Appendix. The routine LOWEST performs a locally weighted least squares linear regression on a set of n (x,y) data pairs where the weights are functions of the distance d from the point to be smoothed. The routine returns the y-estimate obtained from a clever modification of the usual formula for least squares regression.
Local Weighted Regression – Cleveland’s Method.pdf
LOWESS/LOESS For Surveyors
Lowess (locally weighted scatterplot smoothing) is a robust weighted regression smoothing algorithm introduced by William S. Cleveland in 1979. The procedure uses M-estimation, incorporating Iteratively Reweighted Least Squares and is particularly useful in showing smoothed values of the dependent y-variable in x,y scatterplots. Loess (locally weighted regression) was introduced by Cleveland and Susan J. Devlin in 1988 as an extension of Lowess – but without M-estimation – applied to the estimation of regression surfaces. The aim of this article is to show, through examples, how the theory of least squares and M-estimation is applied to regression analysis.
LOWESS for Surveyors.pdf
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