Asymptotics of selective inference. (English) Zbl 1422.62252

Tian, Xiaoying; Taylor, Jonathan

Scand. J. Stat. 44, No. 2, 480-499 (2017).

Summary: 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 selective inference along the solution path of the least absolute shrinkage and selection operator (LASSO), as well as selective inference after fitting the least absolute shrinkage and selection operator at a fixed value of the regularization parameter. We also consider some tests in penalized generalized linear models. Our result proves asymptotic convergence in the high-dimensional setting where \(n<p\), and \(n\) can be of a logarithmic factor of the dimension \(p\) for some procedures.

MSC:

62J07	Ridge regression; shrinkage estimators (Lasso)
62H12	Estimation in multivariate analysis

Keywords:

high-dimensional inference; LASSO; non-Gaussian error; selective inference; least absolute shrinkage and selection operator