Uniform Inference in High-Dimensional Threshold Regression Models

Abstract

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1 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 model is a linear or threshold regression. Additionally, we extend the theory to accommodate time series data under the near-epoch dependence assumption. Finally, we identify statistically significant factors influencing cross-country economic growth and quantify the effects of military news shocks on US government spending and GDP, while also estimating a data-driven threshold point in both applications.