Change Point Detection For Small Samples Under Intercept Sampling Method

With the development of big data technology,the research on sequence is gradually deepened,at the same time,the actual demand of manufacturing industry for product quality control makes the problem of sequence change-point detection become a hot research direction.As one of the classic statistical models,the study of the mean change-point of the independent identically distributed random variable sequence under the normal population assumption lays the foundation for the development of change-point detection.Subsequently,variance change-points,persistence change-points and other change-point types were proposed in succession,the academic community widely targeted at models,test statistics,and algorithm and program improvements,or pioneered methods,making change-point detection applicable to a wider range of fields.However,compared with other sampling methods,new sampling methods have little development.Based on small sample change-point detection,this paper innovates the sampling method.For the same group of observation data,the difference of observation start and end time should not cause large fluctuations in the detected change-point position,that is,the detected change-point position should be consistent to a large extent.Based on this,this paper proposes the interception sampling method.In order to illustrate that the sampling method is applicable to the detection of change-points,Wilcoxon rank sum test,kernel function method and Bayes least squares method are selected.Among them,Wilcoxon rank sum test,as a non-parametric method,is often used to detect whether two groups of independent samples are from the same population;from the perspective of Hilbert space,the kernel function method gives the conditions that the change-point should meet,and should have greater accuracy in each specific situation;Bayes least squares method is a new method proposed in this paper,only for comparison.This paper is arranged as follows:In the first chapter,the development process and recent scientific research achievements of change-point detection are reviewed;In the second chapter,the definitions of sampling methods and three detection methods,namely,intercepting sampling method and Wilcoxon rank sum test,kernel function method and Bayes least squares method,are stated and some theoretical proofs are given;Then,in the numerical simulation environment,that is,the third chapter shows the detection effect of the interception sampling method under three sample sizes,and the relationship between the detection effect after the fixed sample size and the change amplitude of the mean value before and after the change-point shows the numerical simulation effect,because the change-point position is known in the numerical simulation environment,the three detection methods are tested,and have achieved good results;In the fourth chapter,the annual flow of the Nile from 1871 to 1970 and the annual change of PM_2.5 concentration from 1979 to 2018 are analyzed to illustrate the actual effect;Finally,a summary and outlook were made.