Inference in high-dimensional regression models without the exact or $L^p$ sparsity
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- asymptotic normality, which is shown to hold without requiring the exact sparsity condition or the 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.
Cite
@article{arxiv.2108.09520,
title = {Inference in high-dimensional regression models without the exact or $L^p$ sparsity},
author = {Jooyoung Cha and Harold D. Chiang and Yuya Sasaki},
journal= {arXiv preprint arXiv:2108.09520},
year = {2023}
}