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Statistical inference and large-scale multiple testing for high-dimensional regression models

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A Discussion to this article was published on 18 December 2023

A Discussion to this article was published on 11 December 2023

A Discussion to this article was published on 07 November 2023

A Discussion to this article was published on 03 November 2023

Abstract

This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence intervals and hypothesis tests for various low-dimensional objectives such as regression coefficients and linear and quadratic functionals. The key technique is to generate debiased and desparsified estimators for the targeted low-dimensional objectives and estimate their uncertainty. In addition to covering the motivations for and intuitions behind these statistical methods, we also discuss their optimality and adaptivity in the context of high-dimensional inference. In addition, we review the recent development of statistical inference based on multiple regression models and the advancement of large-scale multiple testing for high-dimensional regression. The R package SIHR has implemented some of the high-dimensional inference methods discussed in this paper.

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Acknowledgements

The research of Yin Xia was supported in part by NSFC Grant 12022103. The research of Tony Cai was supported in part by NSF Grant DMS-2015259 and NIH grant R01-GM129781.The research of Zijian Guo was partly supported by the NSF grants DMS 1811857 and 2015373 and NIH grants R01GM140463 and R01LM013614.

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  1. Department of Statistics and Data Science, University of Pennsylvania, Philadelphia, USA

    T. Tony Cai

  2. Department of Statistics, Rutgers University, Piscataway, USA

    Zijian Guo

  3. Department of Statistics and Data Science, Fudan University, Shanghai, China

    Yin Xia

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  1. T. Tony Cai
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Correspondence to Yin Xia.

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Cai, T.T., Guo, Z. & Xia, Y. Statistical inference and large-scale multiple testing for high-dimensional regression models. TEST 32, 1135–1171 (2023). https://doi.org/10.1007/s11749-023-00870-1

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