19 Review about estimation of change points

Abstract

This chapter provides an overview of estimation of change points. The chapter discusses the statistical inference problem about a change point model: (1) to determine if any change point should exist in the sequence; and (2) estimate the number and position(s) of change point(s), and other qualities of interest which are related to the change (for example, the magnitude of the jump of the mean). In a way, the classical two-sample and multi-sample problem can be considered as a special case of the general change point problem described in the chapter. The important difference lies in that in the classical case the possible positions of change are precisely known in advance, while in the other formulation, the most important question is to determine these possible positions. The chapter presents various non-Bayesian estimators about jump change model, Bayesian methods, and some other methods are proposed to study the estimates of change points such as dynamic program and smooth approximation.