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Pré-Publication, Document De Travail Année : 2022

A new procedure for Selective Inference with the Generalized Linear Lasso

Yohann de Castro

Résumé

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.
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Dates et versions

hal-03622196 , version 1 (28-03-2022)
hal-03622196 , version 2 (31-07-2022)
hal-03622196 , version 3 (04-07-2023)

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Quentin Duchemin, Yohann de Castro. A new procedure for Selective Inference with the Generalized Linear Lasso. 2022. ⟨hal-03622196v1⟩
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