The Annals of Statistics

Exact post-selection inference, with application to the lasso

Jason D. Lee, Dennis L. Sun, Yuekai Sun, and Jonathan E. Taylor

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We develop a general approach to valid inference after model selection. At the core of our framework is a result that characterizes the distribution of a post-selection estimator conditioned on the selection event. We specialize the approach to model selection by the lasso to form valid confidence intervals for the selected coefficients and test whether all relevant variables have been included in the model.

Article information

Ann. Statist. Volume 44, Number 3 (2016), 907-927.

Received: January 2015
Revised: September 2015
First available in Project Euclid: 11 April 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F03: Hypothesis testing 62J07: Ridge regression; shrinkage estimators
Secondary: 62E15: Exact distribution theory

Lasso confidence interval hypothesis test model selection


Lee, Jason D.; Sun, Dennis L.; Sun, Yuekai; Taylor, Jonathan E. Exact post-selection inference, with application to the lasso. Ann. Statist. 44 (2016), no. 3, 907--927. doi:10.1214/15-AOS1371.

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