Local regression: Difference between revisions

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Local regression and closely related procedures have a long and rich history, having been discovered and rediscovered in different fields on multiple occasions. An early work by [[Robert Henderson (mathematician)|Robert Henderson]]<ref>Henderson, R. Note on Graduation by Adjusted Average. Actuarial Society of America Transactions 17, 43--48. [https://archive.org/details/transactions17actuuoft archive.org]</ref> studying the problem of graduation (a term for smoothing used in Actuarial literature) introduced local regression using cubic polynomials, and showed how earlier graduation methods could be interpreted as local polynomial fitting. [[William S. Cleveland]] and [[Catherine Loader]] (1995);<ref>{{cite Q|Q132138257}}</ref> and [[Lori Murray]] and [[David Bellhouse (statistician)|David Bellhouse]] (2019)<ref>{{cite Q|Q127772934}}</ref> discuss more of the historical work on graduation.

The [[Savitzky-Golay filter]], introduced by [[Abraham Savitzky]] and [[Marcel J. E. Golay]] (1964)<ref>{{cite Q|Q56769732}}</ref> significantly expanded the method. Like the earlier graduation work, thetheir 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 1970s; for example, [[Charles Joel Stone|Charles J. Stone]] (1977),<ref>{{cite Q|Q56533608}}</ref> [[Vladimir Katkovnik]] (1979)<ref>{{citation |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 name="cleve79">{{cite Q|Q30052922}}</ref> Katkovnik (1985)<ref name="katbook">{{cite Q|Q132129931}}</ref> is the earliest book devoted primarily to local regression methods.