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Uniform Inference in High-Dimensional Threshold Regression Models

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  • Jiatong Li
  • Hongqiang Yan

Abstract

We develop uniform inference for high-dimensional threshold regression parameters, allowing for either cross-sectional or time series data. We first establish Oracle inequalities for prediction errors and $\ell_1$ estimation errors for the Lasso estimator of the slope parameters and the threshold parameter, accommodating heteroskedastic non-subgaussian error terms and non-subgaussian covariates. Next, we derive the asymptotic distribution of tests involving an increasing number of slope parameters by debiasing (or desparsifying) the Lasso estimator in cases with no threshold effect and with a fixed threshold effect. We show that the asymptotic distributions in both cases are the same, allowing us to perform uniform inference without specifying whether the true model is a linear or threshold regression. Finally, we demonstrate the consistent performance of our estimator in both cases through simulation studies, and we apply the proposed estimator to analyze two empirical applications.

Suggested Citation

  • Jiatong Li & Hongqiang Yan, 2024. "Uniform Inference in High-Dimensional Threshold Regression Models," Papers 2404.08105, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2404.08105
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    References listed on IDEAS

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    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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