Inference about the change-point in a sequence of random variables

Abstract

Summary Inference is considered about the point in a sequence of random variables at which the probability distribution changes. In particular, we examine a normal distribution with changing mean. The asymptotic distribution of the maximum likelihood estimate is derived and also the asymptotic distribution of the likelihood ratio statistic for testing hypotheses about the change-point. These asymptotic distributions are compared with some finite sample empirical distributions.