Simultaneous Inference for High-Dimensional Linear Models

• 成果类型: Article
• 署名作者: Zhang, Xianyang; Cheng, Guang
• 署名单位: Texas A&M University System; Texas A&M University College Station; Purdue University System; Purdue University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1166114
• 发表日期: 2017
• 页码: 757-768
• 关键词: 2-sample test; selection; tests; INDEPENDENCE

摘要

This article proposes a bootstrap-assisted procedure to conduct simultaneous inference for high-dimensional sparse linear models based on the recent desparsifying Lasso estimator. Our procedure allows the dimension of the parameter vector of interest to be exponentially larger than sample size, and it automatically accounts for the dependence within the desparsifying Lasso estimator. Moreover, our simultaneous testing method can be naturally coupled with the margin screening to enhance its power in sparse testing with a reduced computational cost, or with the step-down method to provide a strong control for the family-wise error rate. In theory, we prove that our simultaneous testing procedure asymptotically achieves the prespecified significance level, and enjoys certain optimality in terms of its power even when the model errors are non-Gaussian. Our general theory is also useful in studying the support recovery problem. To broaden the applicability, we further extend our main results to generalized linear models with convex loss functions. The effectiveness of our methods is demonstrated via simulation studies. Supplementary materials for this article are available online.