# lasso and cross-validation (theoretical results)

is there any theoretical result which says that use the minimum of the cross-validation as value for the lasso penalty is a good choice?

I would like something like $P(S_0 \subset \hat S_{lasso}(\lambda_{cv}))\rightarrow 1$ where $S_0$ is the set of true variable.

Where can I find it?

• This is a pretty generic question about generalization error and empirical risk minimization. – hearse May 8 '13 at 16:42
• In the book statistics for high dimensional data they said :" The empirical fact that often $S_0\subset \hat S$ is supported by theory. " Where can I found that theory? – Donbeo May 8 '13 at 16:51

The property that you're looking for is sometimes called the "oracle property": Can we estimate the true subset $$S_0$$ of variables with increasing number of observations $$n$$?