Local regression: Difference between revisions

Revision as of 01:58, 7 September 2007

Revision as of 04:46, 6 June 2008

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==Definition of a LOESS model==

LOESS, originally proposed by Cleveland (1979)<!-- Please list this in a "References" section below. --> and further developed by Cleveland and Devlin (1988)<!-- Please list this in a "References" section below. -->, specifically denotes a method that is (somewhat) more descriptively known as locally weighted polynomial regression. At each point in the [[data set]] a low-degree [[polynomial]] is fit to a subset of the data, with [[explanatory variable]] values near the point whose [[response variable|response]] is being estimated. The polynomial is fit using [[weighted least squares]], giving more weight to points near the point whose response is being estimated and less weight to points further away. The value of the regression function for the point is then obtained by evaluating the local polynomial using the explanatory variable values for that data point[[datum]]. The LOESS fit is complete after regression function values have been computed for each of the <math>n</math> data points. Many of the details of this method, such as the degree of the polynomial model and the weights, are flexible. The range of choices for each part of the method and typical defaults are briefly discussed next.

==Localized subsets of data==