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Inference in high-dimensional regression models without the exact or $L^p$ sparsity

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  • Jooyoung Cha
  • Harold D. Chiang
  • Yuya Sasaki

Abstract

This paper proposes a new method of inference in high-dimensional regression models and high-dimensional IV regression models. Estimation is based on a combined use of the orthogonal greedy algorithm, high-dimensional Akaike information criterion, and double/debiased machine learning. The method of inference for any low-dimensional subvector of high-dimensional parameters is based on a root-$N$ asymptotic normality, which is shown to hold without requiring the exact sparsity condition or the $L^p$ sparsity condition. Simulation studies demonstrate superior finite-sample performance of this proposed method over those based on the LASSO or the random forest, especially under less sparse models. We illustrate an application to production analysis with a panel of Chilean firms.

Suggested Citation

  • Jooyoung Cha & Harold D. Chiang & Yuya Sasaki, 2021. "Inference in high-dimensional regression models without the exact or $L^p$ sparsity," Papers 2108.09520, arXiv.org, revised Dec 2022.
  • Handle: RePEc:arx:papers:2108.09520
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    References listed on IDEAS

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