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.

中文翻译：

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稳健的弯曲线回归


我们引入了具有未知变化点的基于排序的弯曲线性回归。使用线性重新参数化技术，我们提出了一种基于排名的估计，可以以计算有效的方式同时推断所有模型参数，包括变化点的位置。我们还基于加权 CUSUM 过程开发了一种类似于分数的测试来判断是否存在变化点。该检验仅需要在没有变化点的情况下在原假设下拟合模型，因此它在计算上比似然比类型检验更有效。检验的渐近性质是在零模型和局部替代模型下导出的。仿真研究和两个真实数据示例表明，所提出的方法对于参数估计和假设检验中的异常值和重尾误差具有鲁棒性。