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Confidence intervals and regions for the lasso by using stochastic variational inequality techniques in optimization
Author(s) -
Lu Shu,
Liu Yufeng,
Yin Liang,
Zhang Kai
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12184
Subject(s) - lasso (programming language) , inference , statistical inference , confidence interval , mathematical optimization , computer science , mathematics , feature selection , selection (genetic algorithm) , algorithm , artificial intelligence , statistics , world wide web
Summary Sparse regression techniques have been popular in recent years because of their ability in handling high dimensional data with built‐in variable selection. The lasso is perhaps one of the most well‐known examples. Despite intensive work in this direction, how to provide valid inference for sparse regularized methods remains a challenging statistical problem. We take a unique point of view of this problem and propose to make use of stochastic variational inequality techniques in optimization to derive confidence intervals and regions for the lasso. Some theoretical properties of the procedure are obtained. Both simulated and real data examples are used to demonstrate the performance of the method.