State-of-the-Art Review

Abstract

The change-point problem can be considered to be one of the central problems of statistical inference, linking together statistical control theory, the theory of estimation and testing hypotheses, classical and Bayesian approaches, and fixed’ sample and sequential procedures. The first publications of Page [117,118], and Girshick and Rubin [57] already appeared in the 1950s in connection with industrial quality control (Shewhart’s chart, CUSUM test). But it was at the end of the 1950s that the change-point problem was formulated in a precise mathematical sense by A.N.Kolmogorov. This problem of optimal sequential change-point detection was solved by A.N.Shiryaev [150,153], who proposed Bayesian and minimax solutions both for discrete and continuous time. The change-point problem was then intensively investigated in the works of Lorden, Hinkley, Zacks, Telksnys and Kligiene and others. Nowadays, this field of statistical research looks like a large family of mathematical problems reflecting different approaches to the main question: is the sample of observations homogenous in a statistical sense? If the answer is no, then what segments of homogeneity exist in the given sample?