en>Dolphin51: Changed linking to avoid Centrifugal - a disambiguation page.

2013-01-29T05:32:25Z

Changed linking to avoid Centrifugal - a disambiguation page.

← Older revision		Revision as of 07:32, 29 January 2013
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			In [[statistics]], an '''additive model''' ('''AM''') is a [[nonparametric regression]] method. It was suggested by [[Jerome H. Friedman]] and Werner Stuetzle (1981)<ref>[[Friedman, J.H.]] and Stuetzle, W. (1981). "Projection Pursuit Regression", ''Journal of the American Statistical Association'' 76:817–823. {{doi\|10.1080/01621459.1981.10477729}}</ref> and is an essential part of the [[Alternating conditional expectation model\|ACE]] algorithm. The ''AM'' uses a one dimensional [[Smoothing\|smoother]] to build a restricted class of nonparametric regression models. Because of this, it is less affected by the [[curse of dimensionality]] than e.g. a ''p''-dimensional smoother. Furthermore, the ''AM'' is more flexible than a [[linear regression\|standard linear model]], while being more interpretable than a general regression surface at the cost of approximation errors. Problems with ''AM'' include [[model selection]], [[overfitting]], and [[multicollinearity]].

			==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>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>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 [[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>

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			*[[Generalized additive model]]
			*[[Backfitting algorithm]]
			*[[Alternating conditional expectation model]]
			*[[Projection pursuit regression]]
			*[[Generalized additive model for location, scale, and shape]] (GAMLSS)
			*[[Median polish]]

			==References==
			{{reflist}}

			==Further reading==
			*Breiman, L. and [[Friedman, J.H.]] (1985). "Estimating Optimal Transformations for Multiple Regression and Correlation", ''[[Journal of the American Statistical Association]]'' 80:580–598. {{doi\|10.1080/01621459.1985.10478157}}

			[[Category:Regression analysis]]
			[[Category:Nonparametric regression]]

en>Mild Bill Hiccup: spelling

2011-12-27T09:44:21Z

spelling

New page

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Vibration of rotating structures - Revision history

en>Dolphin51: Changed linking to avoid Centrifugal - a disambiguation page.

en>Mild Bill Hiccup: spelling