Nonparametric Optimal Tests for Threshold Regression Models in Short Panels

This article focuses on detecting the threshold regression model in short panel data. Utilizing the local asymptotic normality property, we propose nonparametric procedures that are both locally and asymptotically optimal for testing the traditional regression model against the threshold regression model, following the Le Cam and Hájek criteria. We introduce rank-based tests that are asymptotically most stringent and valid across a broad range of density functions. Additionally, we derive the asymptotic relative efficiencies in comparison to Gaussian parametric tests. Numerical simulations and real data demonstrate the strong performance of the proposed tests.