# Change-point Detection by the Quantile LASSO Method

## TL;DR

This paper introduces a quantile LASSO method for change-point detection in piece-wise constant models that is robust to heavy-tailed errors and can estimate multiple quantiles simultaneously.

## Contribution

The paper presents a novel quantile LASSO approach for change-point detection that does not require traditional distributional assumptions and provides consistent change-point estimates.

## Key findings

- The method effectively handles heavy-tailed error distributions.
- It provides consistent estimates when the number of change-points is correctly identified.
- Numerical simulations demonstrate robustness and empirical performance.

## Abstract

A simultaneous change-point detection and estimation in a piece-wise constant model is a common task in modern statistics. If, in addition, the whole estimation can be performed automatically, in just one single step without going through any hypothesis tests for non-identifiable models, or unwieldy classical a-posterior methods, it becomes an interesting, but also challenging idea. In this paper we introduce the estimation method based on the quantile LASSO approach. Unlike standard LASSO approaches, our method does not rely on typical assumptions usually required for the model errors, such as sub-Gaussian or Normal distribution. The proposed quantile LASSO method can effectively handle heavy-tailed random error distributions, and, in general, it offers a more complex view of the data as one can obtain any conditional quantile of the target distribution, not just the conditional mean. It is proved that under some reasonable assumptions the number of change-points is not underestimated with probability tenting to one, and, in addition, when the number of change-points is estimated correctly, the change-point estimates provided by the quantile LASSO are consistent. Numerical simulations are used to demonstrate these results and to illustrate the empirical performance robust favor of the proposed quantile LASSO method.