Cumulative Ratio For Detection Of Mean Change-Point

Change-Point are widely used.There are many important problems in real life,such as fault detection,diagnosis and monitoring,safety of complex systems(including aircraft,spacecraft,rocket,etc.),quality control,prediction of natural disasters(including earthquakes,tsunamis,etc.)and monitoring in biopharmaceuticals,etc.Solving these problems will bring us great benefits in life safety,ecological environment and economy.One of the common points of these problems is how to detect sudden changes that will lead to structural changes in these processes.And for convenience of study,it is customary to call this change time as Change-Point.In this paper,we propose a new statistic-cumulative sum ratio statistic,to estimate the mean change-point.In Chapter 2.the method of cumulative sum ratio is used to estimate the mean change points,and the consistency of the mean change-point estimation is proved.The simulation results show that when the sample size is 1/2 and 3/4,and the sample size and ? value are selected appropriately,under the simple random sample sequence,the accuracy of the change-point position estimation can almost reach 100%,which proves that the method is effective.In addition,compared with cumulative sum method and the validity of cumulative sum ratio method,the method is also further verified by real data detection.In the third chapter,the method of cumulative sum ratio is used to estimate the mean change-point in panel data,and the consistency of the mean change-point estimation is proved.The numerical simulation results show that the accuracy of the change-point location estimation is higher in the panel data structure than in the one-dimensional data structure.When N is greater than or equal to 200,no matter where the real change-point occurs,as long as the appropriate ? value is selected;the accuracy of the estimation is almost 100%.In particular,when the real change-point T occurs at 1/2 and 3/4 of the sample size,the accuracy of the change-point location estimation is almost independent of the ? value and the sample size N.At the same time,under the panel data structure,the effectiveness of the cumulative sum ratio method is verified by comparing the cumulative sum method with the cumulative sum method.The fourth chapter further verifies the effectiveness of the cumulative sum ratio method through empirical analysis.Finally,this paper summarizes the full text and puts forward further research directions.