Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution

Abstract

The usual mean change-point detecting method based on normal linear regression is not robust to heavy-tailed data with potential outlying points. We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative sampling algorithm from a Bayesian perspective. The algorithm can generate independently and identically distributed samples approximately from the posterior distribution of the position of the change-point, which can be used for statistical inferences straightforwardly. The procedure combines the robustness of quantile regression and the computational efficiency of the non-iterative sampling algorithm. A simulation study is conducted to illustrate the performance of the procedure with satisfying findings, and finally, real data is analyzed to show the usefulness of the algorithm by comparison with the usual change-point detection method based on normal regression.

Introduction to the Special Issue in Symmetry Titled “Symmetry in Statistics and Data Science”

“…10. In their article entitled "Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution", Yang [10] creates a noniterative sampling process from a Bayesian perspective and offers a robust changepoint estimation method based on a quantile regression model with an asymmetric Laplace error distribution. After conducting a simulation study to demonstrate the procedure's effectiveness with encouraging results, real data are studied to demonstrate the algorithm's utility in comparison to the traditional change-point detection approach based on normal regression.…”