  We introduce a rank-based bent linear regression with an unknown change
point. Using a linear reparameterization technique, we propose a rank-based
estimate that can make simultaneous inference on all model parameters,
including the location of the change point, in a computationally efficient
manner. We also develop a score-like test for the existence of a change point,
based on a weighted CUSUM process. This test only requires fitting the model
under the null hypothesis in absence of a change point, thus it is
computationally more efficient than likelihood-ratio type tests. The asymptotic
properties of the test are derived under both the null and the local
alternative models. Simulation studies and two real data examples show that the
proposed methods are robust against outliers and heavy-tailed errors in both
parameter estimation and hypothesis testing.
