# Robust bent line regression

arXiv: https://arxiv.org/abs/1606.02234 · HTML: https://mlsanity.com/paper/1606.02234/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2016.

## Built on by (most cited first, 1 of 1)

- [Segmented Continuous Optimization](https://mlsanity.com/paper/2602.20857/) (2026)

## Abstract (arXiv)

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.