plsdof (version 0.2-1)

gmdl: Generalized minimum description length

Description

This function computes the generalized minimum description length and its argmin.

Usage

gmdl(sigmahat, n, DoF, yhat)

Arguments

sigmahat

vector of estimated model errors.

n

number of observations.

DoF

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

yhat

vector of squared norm of yhat. The length of yhat is the same as the length of sigmahat

Value

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

Details

The gmdl criterion is defined as $$gmdl=\frac{n}{2}log(S)+\frac{DoF}{2}log(F)+\frac{1}{2}log(n)$$ with $$S=\hat \sigma ^2$$ Note that it is also possible to use this function for other regression methods than Partial Least Squares.

References

Hansen, M., Yu, B. (2001). "Model Selection and Minimum Descripion Length Principle". Journal of the American Statistical Association, 96, 746 - 774 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, aic, bic

Examples

## This is an internal function.