Change-point Detection In Mixed Regression Model

Big data era produced a rich data,but how to effectively detect abnormal data in point mu-tation has attracted much attention.The change point detection technology is undoubtedly one of the most effective means to solve this problem,the detection means has been widely applied to economics,climate simulation,bio medicine,various fields of counter-terrorism so,it has impor-tant significance.But with the influence on the autoregressive time series,and the data model of linear covariate regression effect,namely the mixed regression model of existing literature rarely involved.This paper plans mixed regression model change point detection problem is studied.Firstly,some classical literature is briefly reviewed,and the mean value model,autoregres-sive model,regression models were analyzed and summarized,constructs a new model,namely mixed regression model.Then,using the least square method with penalty on model parame-ters are estimated.Considering the sparsity of the change point,we with the help of Group Lasso(Least absolute shrinkage and selection operator)technology will change point estimation problem is transformed variable selection problem,and gives a coordinate descent algorithm for variable points.Then,gives a method of mixed regression model change point detection,the proposed test statistic is given,under certain conditions,the corresponding statistical properties and theory proof.Finally,using simulated data further analysis.The main conclusions of this paper are:under the given conditions,estimate the number of change points is not less than the number of real change in probability tends to 1;change point estimate and the true position,estimation of the model parameters and actual parameters are consistent with(referring to the location of change point under the given conditions,the estimation and estimation true position or model parameters and actual parameters of the absolute value of the difference can be limited in a certain range);if the estimated number of change points is not less than the number of true change points,to estimate the change point sets and real change point set is consistent;in the given information criterion,estimated only with model adjustment the number of parameters related with probability 1 to the number of real variable.The simulation results show that the mixed regression model with the existing three models,can more accurately detect the change point location and number,and high stability,obvious advantages.