Real-time Change Point Detection Of Mixed Models Based On Expectile

In the era of big data,change point detection,as one of the subjects of long-term research in statistics,plays a pivotal role.This paper studies the change points of the coefficients in the model,among which,the error of the model is asymmetric,the number of explanatory variables in the model is very large,and the explained variables have the influence of lag term.In view of these situations,based on the linear expectile proposed by predecessors,this paper further considers the mixed model of linear expectile with the lagged term of the explained variable.Based on this model,the CUSUM of the corresponding residuals is derived by the method of expectile and Adaptive LASSO estimation.The corresponding test statistics were established respectively.To verify the rationality of the test statistics,the asymptotic distribution of the test statistics is obtained when the null hypothesis is established(i.e.,no change point is detected).When the alternative hypothesis holds(i.e.,the change point is detected),it is proved that the statistic diverges.Then the simulation results of other CUSUM statistics are compared through simulation studies.Finally,a further test is made on real data.