Robust bent line regression

TL;DR

This paper proposes a robust, rank-based bent linear regression method with an unknown change point, offering efficient inference and a computationally simple test for change point detection, effective against outliers and heavy-tailed errors.

Contribution

It introduces a novel rank-based estimation technique for bent linear regression with change points, including a new efficient test for change point existence.

Findings

The method is robust against outliers and heavy-tailed errors.

Simulation studies demonstrate accurate parameter estimation.

The test effectively detects change points in real data examples.

Abstract

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.