Detection Of Change-point Near The End Points Of Sequences

The change-point detection is an active research field recently, and has been applied extensively in many fields of study which includes economics, finance, image processing, signal processing and so on. In this thesis, we study a family of cumulative-sum type estimators for change-point detection. We investigate the rate of convergence of the CUSUM-type estimators for some sequences and processes.This thesis is organized as follows.In Chapter one we mainly introduce the background of change-point detection and various approaches used in the previous literature.In Chapter two, we study a kind of generalized CUSUM estimator for the change-point for the independent sequence, the short range dependent sequence (SRD) and the long range dependent sequence (LRD), where the change-point can be tends to one end of the sequence. This CUSUM estimator is defined by a semi-norm of a empirical measure. under very weak dependent structure, by using a non-parametric approach, we prove that it has a convergence rate of 1/n with probability (i.e. Op(n-1)).In Chapter three, we consider a local CUSUM estimator based on local average for a continous process with high frenquency sampling and noise. We proved a preliminary result that it can converge to the change-point with probability when the correlation between adjacent samples does not tend to zero.