NONPENALIZED VARIABLE SELECTION IN HIGH-DIMENSIONAL LINEAR MODEL SETTINGS VIA GENERALIZED FIDUCIAL INFERENCE

• 成果类型: Article
• 署名作者: Williams, Jonathan P.; Hannig, Jan
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1733
• 发表日期: 2019
• 页码: 1723-1753
• 关键词: regression

摘要

Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design matrix is collinear. To overcome this challenge, an entirely new perspective on variable selection is presented within a generalized fiducial inference framework. This new procedure is able to effectively account for linear dependencies among subsets of covariates in a high-dimensional setting where p can grow almost exponentially in n, as well as in the classical setting where p <= n. It is shown that the procedure very naturally assigns small probabilities to subsets of covariates which include redundancies by way of explicit L-0 minimization Furthermore, with a typical sparsity assumption, it is shown that the proposed method is consistent in the sense that the probability of the true sparse subset of covariates converges in probability to 1 as n -> infinity, or as n -> infinity and p -> infinity. Very reasonable conditions are needed, and little restriction is placed on the class of possible subsets of covariates to achieve this consistency result.