information.criteria: Information criteria

Description

This function computes the optimal model parameters using three different model selection criteria (aic, bic, gmdl).

Usage

information.criteria(RSS, DoF, yhat, sigmahat, n,criterion="bic")

Arguments

RSS

vector of residual sum of squares.

DoF

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

yhat

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

sigmahat

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

number of observations.

criterion

one of the options "aic", "bic" and "gmdl".

Value

DoFdegrees of freedom
scorevector of the model selection criterion
parindex of the first local minimum of score

References

Akaikie, H. (1973) "Information Theory and an Extension of the Maximum Likelihood Principle". Second International Symposium on Information Theory, 267 - 281. 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 Schwartz, G. (1979) "Estimating the Dimension of a Model" Annals of Statistics 26(5), 1651 - 1686.

Examples

Run this code

## This is an internal function called by pls.ic