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Are Latent Factor Regression and Sparse Regression Adequate?

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  • Jianqing Fan
  • Zhipeng Lou
  • Mengxin Yu

Abstract

We propose the Factor Augmented (sparse linear) Regression Model (FARM) that not only admits both the latent factor regression and sparse linear regression as special cases but also bridges dimension reduction and sparse regression together. We provide theoretical guarantees for the estimation of our model under the existence of sub-Gaussian and heavy-tailed noises (with bounded (1+ϑ) th moment, for all ϑ>0), respectively. In addition, the existing works on supervised learning often assume the latent factor regression or sparse linear regression is the true underlying model without justifying its adequacy. To fill in such an important gap on high-dimensional inference, we also leverage our model as the alternative model to test the sufficiency of the latent factor regression and the sparse linear regression models. To accomplish these goals, we propose the Factor-Adjusted deBiased Test (FabTest) and a two-stage ANOVA type test, respectively. We also conduct large-scale numerical experiments including both synthetic and FRED macroeconomics data to corroborate the theoretical properties of our methods. Numerical results illustrate the robustness and effectiveness of our model against latent factor regression and sparse linear regression models. Supplementary materials for this article are available online.

Suggested Citation

  • Jianqing Fan & Zhipeng Lou & Mengxin Yu, 2024. "Are Latent Factor Regression and Sparse Regression Adequate?," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1076-1088, April.
  • Handle: RePEc:taf:jnlasa:v:119:y:2024:i:546:p:1076-1088
    DOI: 10.1080/01621459.2023.2169700
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    Cited by:

    1. Beyhum, Jad & Striaukas, Jonas, 2024. "Testing for sparse idiosyncratic components in factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 244(1).
    2. Donggyu Kim & Minseok Shin, 2024. "Nonconvex High-Dimensional Time-Varying Coefficient Estimation for Noisy High-Frequency Observations with a Factor Structure," Working Papers 202418, University of California at Riverside, Department of Economics.

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