Survey of classical and Bayesian approaches to the change-point problem: Fixed sample and sequential procedures of testing and estimation. (English) Zbl 0563.62062

Zacks, S.

Recent advances in statistics, Pap. in Honor of H. Chernoff, 245-269 (1983).

[For the entire collection see Zbl 0517.00012.]
This paper surveys a section of the important developments in the area of the title. It focuses ”on methods for testing the null hypothesis of no change among given n observations, against the alternative of at most one change. Section 2 is devoted to the testing problem in a fixed sample. Section 3 presents Bayesian and maximum likelihood estimation of the location of the shift points. Section 4 is devoted to the sequential detection procedures. We present the basic Bayesian and classical results in this area.... The important area of switching regressions has not been reviewed here in any detail.” The author lists seventy references, and points out that there are several other areas and publications related to the general outlook of the change-point problem.

Reviewer: M.M.Rao

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F15	Bayesian inference
62L10	Sequential statistical analysis
62L12	Sequential estimation
62G10	Nonparametric hypothesis testing
62F10	Point estimation

Keywords:

survey; maximum likelihood estimation; change-point problem