2019/08/04 by Fei Wang, Ling Zhou, Wang, Fei +6
Computer Science · Engineering · Mathematics · #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistics Theory (math.ST) #cs.LG #math.ST #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.1908.01253
arxiv created 2019/08/04 · openalex publication_date 2019/08/04 · arxiv updated 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Simultaneous inference after model selection is of critical importance to address scientific hypotheses involving a set of parameters. In this paper, we consider high-dimensional linear regression model in which a regularization procedure such as LASSO is applied to yield a sparse model. To establish a simultaneous post-model selection inference, we propose a method of contraction and expansion (MOCE) along the line of debiasing estimation that enables us to balance the bias-and-variance trade-off so that the super-sparsity assumption may be relaxed. We establish key theoretical results for the proposed MOCE procedure from which the expanded model can be selected with theoretical guarantees and simultaneous confidence regions can be constructed by the joint asymptotic normal distribution. In comparison with existing methods, our proposed method exhibits stable and reliable coverage at a nominal significance level with substantially less computational burden, and thus it is trustworthy for its application in solving real-world problems.