Local regression: Difference between revisions

Revision as of 07:36, 15 February 2025

Revision as of 09:03, 15 February 2025

Line 20:

The [[Savitzky-Golay filter]], introduced by [[Abraham Savitzky]] and [[Marcel J. E. Golay]] (1964)<ref>{{citeQ|Q56769732}}</ref> significantly expanded the method. Like the earlier graduation work, the focus was on data with an equally-spaced predictor variable, where (excluding boundary effects) local regression can be represented as a [[convolution]]. Savitzky and Golay published extensive sets of convolution coefficients for different orders of polynomial and smoothing window widths.

Local regression methods started to appear extensively in statistics literature in the 1970's; for example, [[Charles Joel Stone|Charles J. Stone]] (1977)<ref>{{citeQ|Q56533608}}</ref>, [[Vladimir Katkovnik]] (1979)<ref>{{cite |first=Vladimir|last=Katkovnik|title=Linear and nonlinear methods of nonparametric regression analysis.|journal=Soviet Automatic Control|date=1979|volume=12|issue=5|pages=25-34}}</ref> and [[William S. Cleveland]] (1979)<ref>{{citeQ|Q30052922}}</ref>. Katkovnik (1985)<ref name="katbook">{{citeQ|Q132129931}}</ref> is the earliest book devoted primarily to local regression methods.

Extensive theoretical work continued to appear throughout the 1990's. Important contributions include [[Jianqing Fan]] and [[Irène Gijbels]] (1992)<ref>{{citeQ|Q132202273}}</ref> studying efficiency properties, and [[David Ruppert]] and [[Matthew P. Wand]] (1994)<ref>{{citeQ|Q132202598}}</ref> developing an asymptotic distribution theory for multivariate local regression.