I am currently working on a method for adaptive knot placement in Spline regression. Following Osborne et.al. (1998), Yuan et.al. (2014) I am interested in using LASSO regression to select a subset of basis and then obtain by means of an algorithm a knot vector. My question regards the penalisation parameter $\lambda$, I've seen some authors that select the value for it according to the 10-fold CV, but I have some doubts regarding this. In this particular case we want to extract a signal, so I am not sure if the CV is the best method for selecting the penalisation, I mean, we are not going to extrapolate our results to a new set of data. In this case wouldn't it be better to use AIC criterium instead?
I am open to any suggestion, and I thank you in advance.