Classical and Bayesian Approaches to the Change-Point Problem: Fixed Sample and Sequential Procedures.

Abstract

Abstract : The change-point problem can be considered one of the central problems of statistical inference, linking together statistical control theory, theory of estimation and testing hypotheses, classical and Bayesian approaches, fixed sample and sequential procedures. It is very often the case that observations are taken sequentially over time, or can be intrinsically ordered in some other fashion. The basic question is, therefore, whether the observations represent independent and identically distributed random variables, or whether at least one change in the distribution law has taken place. This is the fundamental problem in the statistical control theory, testing the stationarity of stochastic processes, estimation of the current position of a time-series, etc. Accordingly, a survey of all the major developments in statistical theory and methodology connected with the very general outlook of the change-point problem, would require review of the field of statistical quality control, the switching regression problems, inventory and queueing control, etc. The present review paper is therefore focused on methods developed during the last two decades for the estimation of the current position of the mean function of a sequence of random variables (or of a stochastic process); testing the null hypothesis of no change among given n observations, against the alternative of at most one change; the estimation of the location of the change-point(s) and some sequential detection procedures.

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