Change-point analysis: Detection, estimation and applications

In this study, the problem of detecting and estimating the unknown, change-point in a sequence of time-ordered observations is considered. The general distribution setup is applied to cases where one or two parameters of a normal or an exponential distribution change, as well as to the case of a Weibull distribution where both shape and scale parameters change.; In chapter 2, we consider the detection problem. Hypothesis testing for no change against a possible change is conducted, employing a maximum likelihood statistic that follows the double-exponential distribution. The associated likelihood ratio test is then implemented in a Minitab macro and coupled with an algorithm that reduces multiple change-point problems to single change-point counterparts, allowing for revisions of the contaminated estimates.; In chapter 3, we consider the estimation problem. Maximum likelihood estimates of the change-point and the parameters before and after it are obtained, and an algorithmic procedure provides a confidence interval for the unknown change-point.; In chapter 4, the methodologies discussed in chapters 2 and 3 are applied to a number of data sets, drawn from the areas of climatology, operations management environmental science, and finance. Some of them have already been examined in the change-point literature and are included here for comparison purposes, and others are introduced in a change-point context for the first time.