Finds initial smoothing parameter guesses for multiple smoothing parameter estimation. The idea is to find values such that the estimated degrees of freedom per penalized parameter should be well away from 0 and 1 for each penalized parameter, thus ensuring that the values are in a region of parameter space where the smoothing parameter estimation criterion is varying substantially with smoothing parameter value.
initial.sp(X,S,off,expensive=FALSE,XX=FALSE)is the model matrix.
is a list of of penalty matrices. S[[i]] is the ith penalty matrix, but note
that it is not stored as a full matrix, but rather as the smallest square matrix including all
the non-zero elements of the penalty matrix. Element 1,1 of S[[i]] occupies
element off[i], off[i] of the ith penalty matrix. Each S[[i]] must be
positive semi-definite.
is an array indicating the first parameter in the parameter vector that is
penalized by the penalty involving S[[i]].
if TRUE then the overall amount of smoothing is
adjusted so that the average degrees of freedom per penalized parameter is
exactly 0.5: this is numerically costly.
if TRUE then X contains \(X^TX\), rather than \(X\).
An array of initial smoothing parameter estimates.
Basically uses a crude approximation to the estimated degrees of freedom per model coefficient, to try and find smoothing parameters which bound these e.d.f.'s away from 0 and 1.