| Change-points problem has always been a hot topic for scholars.In this paper,we use adaptive group Lasso based on the GMD(Groupwise Majorization Descent)algorithm to solve the change-points problem in multiple linear regression models.In terms of computing speed,simulation shows that the algorithm is much faster than sparse group Lasso.In terms of estimation precision,this method can correctly estimate the number of change-points,and the error of change-points position estimation is small.The algorithm also overcomes the problem of clustering in the adaptive Lasso and sparse group Lasso.And this paper gives four reasons why this method outperforms other algorithms in solving change-points problem.First of all,adaptive group Lasso is made up of two-step group Lasso,so it means we filter the change-points twice,which helps to improve the precision of the change-points estimation.Secondly.this paper transforms the change-points problem of linear regression model into the problem of variable selection in high dimensional regression model.The variables have a relatively obvious group structure.And we concern more about the sparsity of group variables than single variable sparsity.Therefore,group Lasso is more suitable for solving this problem than Lasso.Thirdly,we use the GMD algorithm to solve the group Lasso and greatly improve the speed of this method.Finally.the traditional methods firstly estimate the number of change-points,and then they estimate the position of change-points and model parameters.Compared with these methods.our method can estimate them at the same time,which can improve the accuracy of the estimation.In addition,in order to prove the effectiveness of the method in solving practical problems,we apply this algorithm to the real dataset about air quality.We find that air quality improves with the increase of wind force in spring and summer.While there is a negative relationship between air quality and wind force in autumn and winter. |
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