Abstract: We develop a new procedure for testing change points due to a covariate threshold in regression quantiles. The proposed test is based on the CUSUM of the subgradient of the quantile objective function and requires fitting the model only under the null hypothesis. The critical values can be obtained by simulating the Gaussian process that characterizes the limiting distribution of the test statistic. The proposed method can be used to detect change points at a single quantile level or across multiple quantiles, and can accommodate both homoscedastic and heteroscedastic errors. Simulation study suggests that the proposed method has higher computational efficiency and comparable power with the existing likelihood-ratio-based method in the finite samples. The performance of the proposed method is further illustrated by the analysis of a blood pressure and body mass index data set.

Key words and phrases: Change point, covariate threshold, hypothesis testing, quantile regression, threshold regression model.