Asymptotics of selective inference

TL;DR

This paper develops asymptotic results for affine selection procedures in selective inference, extending beyond Gaussian assumptions to include methods like LASSO and penalized generalized linear models.

Contribution

It introduces a new asymptotic framework for affine selection procedures, broadening the scope of selective inference beyond Gaussian models.

Findings

Asymptotic validity for affine selection procedures.

Extension to non-Gaussian models.

Application to LASSO and penalized GLMs.

Abstract

In this paper, we seek to establish asymptotic results for selective inference procedures removing the assumption of Gaussianity. The class of selection procedures we consider are determined by affine inequalities, which we refer to as affine selection procedures. Examples of affine selection procedures include post-selection inference along the solution path of the LASSO, as well as post-selection inference after fitting the LASSO at a fixed value of the regularization parameter. We also consider some tests in penalized generalized linear models. Our method of proof adapts a method of Chatterjee (2005).