Adaptive Group Lasso Penalty Quantile Regression Method For High-dimensional Change-Point Model

With the rapid development of computer technology,people often encounter high-dimensional data in the research.These data not only show obvious heteroscedasticity characteristics,but also forecast variables are grouped.For example,in biological applications,the detected genes or proteins can be grouped into medical pathways by biological action or biological genes.Common statistical analysis methods,such as analysis of variance,factor analysis,and function modeling based on base set,also naturally show variable groupings.In view of high-dimensional data analysis and processing methods,there are many related research literature and methods are more extensive.In many applications,the data set obtained not only has the characteristics of high-dimensional data but also shows the state of heteroscedasticity.At this time,it is more suitable to consider the use of multiphase linear regression model to model each data segment,and each data segment is separated by change points.However,most of the current research on data with change-point characteristics is focused on low-dimensional data,and less attention is paid to high-dimensional data change-point models.In recent years,most of the literatures about change-point model and high-dimensional regression are under the condition of zero mean error and bounded variance.On the other hand,it is well known that the existence of outliers in the model may cause large errors in the leastsquares estimation method.Especially when the error distribution is not Gaussian or thick-tailed,and it is not clear whether the error changes at the two moments before and after the change point,which will cause problems when detecting the change point,it is more suitable to consider quantile regression which has its unique charm in high-dimensional data analysis.In the multiphase model,the change-point estimation may affect the properties of the estimator.The difficulty in studying the change-point model first comes from the correlation of two types of parameters:regression parameters and change-point parameters.However,there are few researches on the quantile change-point regression method for high-dimensional data.In many cases,the solution is to combine the practice first and then get the results through one experiment,which is quite troublesome.Moreover,when the change-point parameter is related to each estimation parameter or the error before and after the change point changes,this method is too complex.Therefore,in order to facilitate the application of practical problems,it is necessary to consider two kinds of parameter problems of the change-point model at the same time,and to simplify the application in high-dimensional problems.In order to study the nature and process of group explanatory variables with high-dimension and change-points,we should not only determine the important groups of regression variables,but also establish a hierarchy between these groups.In regression problems,covariates canbe grouped naturally,and group lasso penalty is an attractive variable selection method because it respects the grouping structure in data.Using the high-dimensional change-point quantile regression,that is,to study the change-point problem when the multiphase model changes,this paper first constructs the high-dimensional change-point quantile regression model and uses the adaptive group Lasso penalty method estimates the parameters of the model's cahnge points and coefficients.Secondly,it studies the asymptotics of the parameter estimators and their Oracle properties,which involves the selection of the related variable groups,without passing the hypothesis test.When the change point is unknown,this paper uses the test method to detect and judge the change point.Finally,Monte Carlo simulation results show that compared with other methods in the literature,this method has better performance in high-dimensional quantile model.Finally,the effectiveness and practicability of the model and method are illustrated by the analysis of the actual data.