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==Description==
Given a [[data]] set <math>\{y_i,\, x_{i1}, \ldots, x_{ip}\}_{i=1}^n</math> of ''n'' [[statistical unit]]s, where <math>\{x_{i1}, \ldots, x_{ip}\}_{i=1}^n</math> represent predictors and <math>y_i</math> is the outcome, the ''additive model'' takes the form
: <math>\mathrm{E}[y_i|x_{i1}, \ldots, x_{ip}] = \beta_0+\sum_{j=1}^p f_j(x_{ij}) </math>
or
: <math>Y= \beta_0+\sum_{j=1}^p f_j(X_{j})+\varepsilon </math>
Where <math>\mathrm{E}[ \epsilon ] = 0</math>, <math>\mathrm{Var}(\epsilon) = \sigma^2</math> and <math>\mathrm{E}[ f_j(X_{j}) ] = 0</math>. The functions <math>f_j(x_{ij})</math> are unknown [[smooth function]]s fit from the data. Fitting the ''AM'' (i.e. the functions <math>f_j(x_{ij})</math>) can be done using the [[backfitting algorithm]] proposed by Andreas Buja, [[Trevor Hastie]] and [[Robert Tibshirani]] (1989).<ref>Buja, A., Hastie, T., and Tibshirani, R. (1989). "Linear Smoothers and Additive Models", ''The Annals of Statistics'' 17(2):453–555. {{jstor|2241560}}</ref>
==See also==
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