Robust Locally Weighted Regression and Smoothing Scatterplots

作者：William S. Cleveland · 发表于：Journal of the American Statistical Association · 年份：1979 · DOI：10.1080/01621459.1979.10481038 · 被引用次数：11101 · 研究领域：Advanced Statistical Methods and Models、Spectroscopy and Chemometric Analyses、Statistical Methods and Inference

The visual information on a scatterplot can be greatly enhanced, with little additional cost, by computing and plotting smoothed points. Robust locally weighted regression is a method for smoothing a scatterplot, (x i , y i ), i = 1, …, n, in which the fitted value at z k is the value of a polynomial fit to the data using weighted least squares, where the weight for (x i , y i ) is large if x i is close to x k and small if it is not. A robust fitting procedure is used that guards against deviant points distorting the smoothed points. Visual, computational, and statistical issues of robust locally weighted regression are discussed. Several examples, including data on lead intoxication, are used to illustrate the methodology.