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Post‐selection inference for ℓ 1 ‐penalized likelihood models
Author(s) -
Taylor Jonathan,
Tibshirani Robert
Publication year - 2018
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11313
Subject(s) - lasso (programming language) , inference , model selection , selection (genetic algorithm) , logistic regression , statistical inference , statistics , econometrics , computer science , mathematics , artificial intelligence , world wide web
We present a new method for post‐selection inference for ℓ 1 (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