= Solution
Choose $(\lambda_1,\lambda_2)$ on a grid by <K-fold cross-validation>, comparing the same held-out prediction loss and optionally applying the one-standard-error rule for a simpler model. A genuinely untouched <test set> can then estimate final prediction error.
Ordinary model-based intervals after selecting nonzero coefficients ignore selection and are generally invalid. Valid approaches include <Debiased Lasso> or a selective-inference procedure under its assumptions, sample splitting followed by an unpenalized refit and inference on the independent half, or a bootstrap that repeats both tuning and fitting and is interpreted with care near the nonsmooth zero threshold.
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