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May 2021 Robust High-Dimensional Factor Models with Applications to Statistical Machine Learning
Jianqing Fan, Kaizheng Wang, Yiqiao Zhong, Ziwei Zhu
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Statist. Sci. 36(2): 303-327 (May 2021). DOI: 10.1214/20-STS785


Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at an ever-growing scale, statistical machine learning faces some new challenges: high dimensionality, strong dependence among observed variables, heavy-tailed variables and heterogeneity. High-dimensional robust factor analysis serves as a powerful toolkit to conquer these challenges.

This paper gives a selective overview on recent advance on high- dimensional factor models and their applications to statistics including Factor-Adjusted Robust Model selection (FarmSelect) and Factor-Adjusted Robust Multiple testing (FarmTest). We show that classical methods, especially principal component analysis (PCA), can be tailored to many new problems and provide powerful tools for statistical estimation and inference. We highlight PCA and its connections to matrix perturbation theory, robust statistics, random projection, false discovery rate, etc., and illustrate through several applications how insights from these fields yield solutions to modern challenges. We also present far-reaching connections between factor models and popular statistical learning problems, including network analysis and low-rank matrix recovery.


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Jianqing Fan. Kaizheng Wang. Yiqiao Zhong. Ziwei Zhu. "Robust High-Dimensional Factor Models with Applications to Statistical Machine Learning." Statist. Sci. 36 (2) 303 - 327, May 2021.


Published: May 2021
First available in Project Euclid: 19 April 2021

Digital Object Identifier: 10.1214/20-STS785

Keywords: Covariance estimation , factor model , FarmSelect , FarmTest , PCA , perturbation bounds , random sketch , robustness

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.36 • No. 2 • May 2021
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