  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).
