Is it appropriate to apply predictive modeling variable selection and shrinkage techniques (for example, ridge regression or lasso) for in-sample prediction rather than out-of-sample prediction? Perhaps using 5- or 10-fold cross validation?
I think this would boil down to using a ridge regression or lasso to build an explanatory model minimizing mean squared error.
If your question is "can I use cross-validation on my training set to find the right shrinkage parameter in ridge regression or lasso", the answer is yes. CV does just that: it separates your data into training and validation sets, so that in each iteration you have "out of sample" observations.
However, you would still need other out of sample data to get a good estimate of prediction error once the model has been optimized by CV.
