Abstract: In the classical setting of the change-point estimation problem, where there is no consistent procedure, a lower bound on the limit of the maximum of error probabilities is established. This bound is attained by the maximum likelihood estimator when the two probability distributions before and after the change-point are known. The minimaxity of the maximum likelihood procedure in the sense of attaining the mentioned bound is proved for observations from an exponential family.
Key words and phrases: Change-point problem, error probability, exponential family, maximum likelihood procedure, minimaxity.