plsdof (version 0.2-1)

aic: Akaike Information Criterion

Description

This function computes the Akaike Information Criterion and its argmin.

Usage

aic(RSS, n, DoF, sigmahat)

Arguments

RSS

vector of residual sum of squares.

n

number of observations.

DoF

vector of Degrees of Freedom. The length of DoF is the same as the length of RSS.

sigmahat

Estimated model error. The length of sigmahat is the same as the length of RSS.

Value

• score
  the vector of the aic values
• par
  index of the first local minimum of score

Details

The aic criterion is defined as $${aic}= \frac{{RSS}}{n} + 2\frac{{DoF}}{n} \sigma^ 2\,.$$ Note that it is also possible to use this function for other regression methods than Partial Least Squares.

References

Akaikie, H. (1973) "Information Theory and an Extension of the Maximum Likelihood Principle". Second International Symposium on Information Theory, 267 - 281. Kraemer, N., Sugiyama M. (2010). "The Degrees of Freedom of Partial Least Squares Regression". preprint, http://arxiv.org/abs/1002.4112 Kraemer, N., Braun, M.L. (2007) "Kernelizing PLS, Degrees of Freedom, and Efficient Model Selection", Proceedings of the 24th International Conference on Machine Learning, Omni Press, 441 - 448

See Also

information.criteria, pls.ic, bic, gmdl

Examples

## this is an internal function called by information.criteria() and pls.ic()