Additive model: Difference between revisions

Revision as of 01:00, 18 October 2012

Revision as of 20:49, 26 January 2013

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or

: <math>Y= \beta_0+\sum_{j=1}^p f_j(X_{j})+\varepsilon </math>

Where <math>E[ \epsilon ] = 0</math>, <math>Var(\epsilon) = \sigma^2</math> and <math>E[ f_j(X_{j}) ] = 0</math>. The functions <math>f_j(x_{ij})</math> are unknown [[Smoothsmooth function|smooth functions]]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.</ref>

==See also==

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{{reflist}}

==Further Readingreading==

*Breiman, L. and Friedman, J.H. (1985). "Estimating Optimal Transformations for Multiple Regression and Correlation", ''[[Journal of the American Statistical Association]]'' 80:580&ndash;598.