Method of Contraction-Expansion (MOCE) for Simultaneous Inference in Linear Models
This addresses the need for reliable post-selection inference in high-dimensional statistics, offering a computationally efficient solution for real-world applications, though it is incremental as it builds on debiasing estimation methods.
The paper tackles the problem of simultaneous inference after model selection in high-dimensional linear regression, proposing the Method of Contraction-Expansion (MOCE) to relax super-sparsity assumptions and achieve stable coverage at nominal significance levels with reduced computational burden.
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.