Sequential Monitoring Coefficient Change In Linear Regression Model

In recent years,the hot topic of research in statistics is the problem of change points that exist in many fields such as economy,finance and medicine.Quickly detecting and alarming the change point at any time are important to reduce losses and risks.This paper mainly studies sequential monitoring coefficient change in linear regression model.Firstly,based on the least squares residues sum of squares,the paper proposes two ratio-type detectors to sequentially monitor coefficient change in linear regression model to avoid estimating the long run variance of samples and improve the stability of monitoring.It investigates the limit distribution of two statistics under the null hypothesis and the consistency under alternative hypothesis.Some critical values are tabulated.Simulations demonstrate that the proposed procedures have higher powers but longer ARLs.Secondly,the point that divided the monitoring data into two part is change point,only if the sum of the least squares residues sum of squares by two data is minimum.The paper proposes an improved ratio-type detector to sequentially monitor coefficient change in linear regression model to maintain the advantage of powers while reducing ARLs as short as possible.It investigates the asymptotic property of the statistic under the null hypothesis and alternative hypothesis.Some sizes,powers and ARLs are tabulated.Finally,the application of the example demonstrates the validity of the proposed procedures.