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Activity Number: 34 - Linear Models for Large or Complex Data
Type: Contributed
Date/Time: Sunday, July 29, 2018 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #327088 Presentation
Title: Significance Testing in Non-Sparse High-Dimensional Linear Models
Author(s): Yinchu Zhu* and Jelena Bradic
Companies: University of Oregon and UC San Diego
Keywords: high-dimensional inference; sparse models; dense models
Abstract:

In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in practice, sparsity assumption is not checkable and more importantly is often violated, with a large number of covariates expected to be associated with the response, indicating that possibly all, rather than just a few, parameters are non-zero. We show that existing inferential methods are sensitive to the sparsity assumption, and may, in turn, result in the severe lack of control of Type-I error. In this article, we propose a new inferential method, named CorrT, which is robust to model misspecification and adaptive to the sparsity assumption. CorrT is shown to have Type I error approaching the nominal level for any models and Type II error approaching zero for sparse and many dense models. In fact, CorrT is also shown to be optimal in a variety of frameworks: sparse, non-sparse and hybrid models where sparse and dense signals are mixed. Numerical experiments show a favorable performance of the CorrT test compared to the state-of-the-art methods.


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