Quantile Variable Point Detection In Mixed Regression Model

Change-point problem is widely used in signal processing,climate,network flow data analysis and many other fields.The primary work of change-point estimation can be traced back to the deviation of the mean value of positioning variables in industrial quality control.With the advent of the information age,massive amounts of data are produced.However,as an important data analysis method and tool,change-point estimation has been widely used in both theoretical and practical applications.The change point problem has also been concerned and studied by many scholars.How to effectively detect and estimate abnormal mutation points in massive data has become the focus of people's attention and has important research significance.In this paper,the mixed regression model is considered,that is,on the basis of the linear regression model proposed by predecessors,the model with the lag term of explained variables is further considered.We used quantile regression method to change point estimation of mixed regression model,will first change point estimation problem is converted into variable selection problem,and second,respectively,with quantile l₂punishment and quantile fused lasso to change point estimation of mixed regression model,finally,we concluded that the estimated statistical properties and simulation is used to demonstrate the effectiveness of the method.Theory,under certain assumptions,we prove the estimate of the change point position is con-sistent,estimation of regression parameters at a certain speed of convergence to the true value,es-timated by the change point set with real change point set of Hausdorff distance can be controlled within a certain range,and estimates the change points is not less than the real change points in probability to 1;In numerical simulation,with the increase of sample size,we get:1)The mean square error of parameters estimated by the two methods decreases gradually,and when the random error term is not normal,the proposed method is superior to the existing method;2)The probability of change points estimated by the two methods including real change points increases gradually.