Lower bound for the Degrees of Freedom

This function computes the lower bound for the the Degrees of Freedom of PLS with 1 component.

Usage

compute.lower.bound(X)

Arguments

X: matrix of predictor observations.

Value

bound: logical. bound is TRUE if the decay of the eigenvalues is slow enough
lower.bound: if bound is TRUE, this is the lower bound, otherwise, it is set to -1

Details

If the decay of the eigenvalues of cor(X) is not too fast, we can lower-bound the Degrees of Freedom of PLS with 1 component. Note that we implicitly assume that we use scaled predictor variables to compute the PLS solution.

References

Kraemer, N., Sugiyama M. (2011). "The Degrees of Freedom of Partial Least Squares Regression". Journal of the American Statistical Association 106 (494) https://www.tandfonline.com/doi/abs/10.1198/jasa.2011.tm10107

Author

Nicole Kraemer

Examples


# Boston Housing data
library(MASS)
data(Boston)
X<-Boston[,-14]
my.lower<-compute.lower.bound(X)