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Asymptotics of Selective Inference
Author(s) -
Tian Xiaoying,
Taylor Jonathan
Publication year - 2017
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12261
Subject(s) - mathematics , inference , affine transformation , lasso (programming language) , selection (genetic algorithm) , regularization (linguistics) , logarithm , pure mathematics , artificial intelligence , mathematical analysis , computer science , world wide web
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 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.