Additive model: Difference between revisions

Revision as of 03:01, 20 March 2022

Revision as of 23:08, 6 February 2023

Line 6:

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&ndash;555. {{jstorJSTOR|2241560}}</ref>

==See also==