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Post‐selection inference for ℓ1 ‐penalized likelihood models

We present a new method for post‐selection inference for ℓ1 (lasso)'penalized likelihood models, including generalized regression models. Our approach generalizes the post‐selection framework presented in Lee et al. (2013). The method provides P‐values and confidence intervals that are asymptotically valid, conditional on the inherent selection done by the lasso. We present applications of this work to (regularized) logistic regression, Cox's proportional hazards model, and the graphical lasso. We do not provide rigorous proofs here of the claimed results, but rather conceptual and theoretical sketches. The Canadian Journal of Statistics 46: 41–61; 2018 © 2017 Statistical Society of Canada