A new procedure for Selective Inference with the Generalized Linear Lasso

03/29/2022

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by   Quentin Duchemin, et al.

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This articles investigates the distribution of the solutions of the generalized linear lasso (GLL), conditional on some selection event. In this framework of post-selection inference (PSI), we provide rigorous definitions of the selected and saturated models: two different paradigms that determine the hypothesis being tested. Based on a conditional Maximum Likelihood Estimator (MLE) approach, we give a procedure to obtain asymptotically valid PSI confidence regions and testing procedures for Generalized Linear Models (GLMs). In a second stage, we focus on the sparse logistic regression and we exhibit conditions ensuring that our conditional MLE method is valid. We present extensive numerical simulations supporting our theoretical results.