A Robust Covariate-Dependent Kink Threshold Regression Model for Panel Data

This paper introduces a rank-based panel kink threshold regression model with a covariate-dependent threshold, where the threshold is specified as a function of informative covariates. To estimate the model parameters, we propose a profile estimation procedure for both the threshold parameters and regression coefficients. Additionally, we develop a Wald test statistic to examine the constancy of the threshold and a sup-score test to detect the presence of the kink effect. Through simulation studies and an empirical analysis, we demonstrate that the proposed methods exhibit robustness against outliers and heavy-tailed errors in both parameter estimation and hypothesis testing.