Estimation Of Multiple Change-Points Models Based On Bayesian Adaptive Group Lasso

Over the past 60 years,change-point problem is one of the hot issues in statistics,econometrics,signal processing,bioinformatics and so on.In this paper,we consider a linear regression model where the coefficients suddenly change at one unknown time.The early literatures give the method that firstly determine the number of change-points,and then estimate the locations of change-points.In recent years,there appears a differen-t method to study the structural changes in linear regression models,which converts the change-point problems with penalty into variable selection problems.This method can si-multaneously estimate the number and locations of change-points,and the coefficient of regression with higher precision.Based on the method of group fused Lasso,proposed by Qian and Su(2015),this paper dose the shrinkage estimation of regression model with multiple change-points under the Bayesian framework.In this paper,we propose the method of Bayesian adaptive group Lasso to estimate the number and locations of change-points in linear regression,and use spike and slab prior for group variable selection.The specific approach is to consider the least squares optimization problem with l2 penalty,give its corresponding Bayesian interpretation by choosing mixture priors with point mass at zero,infer its posterior distribution,and estimate the parameters of posterior distribution using posterior median with MCMC sampling algorithm.Finally,we study the cases of one-break and multi-breaks respectively,and compare the results of the method of Bayesian adaptive group Lasso and the method of group fused Lasso.Simulation shows that our proposed method outperforms the later one.