  In this paper we consider change-points in multiple sequences with the
objective of minimizing the estimation error of a sequence by making use of
information from other sequences. This is in contrast to recent interest on
change-points in multiple sequences where the focus is on detection of common
change-points. We start with the canonical case of a single sequence with
constant change-point intensities. We consider two measures of a change-point
algorithm. The first is the probability of estimating the change-point with no
error. The second is the expected distance between the true and estimated
change-points. We provide a theoretical upper bound for the no error
probability, and a lower bound for the expected distance, that must be
satisfied by all algorithms. We propose a scan-CUSUM algorithm that achieves
the no error upper bound and come close to the distance lower bound. We next
consider the case of non-constant intensities and establish sharp conditions
under which estimation error can go to zero. We propose an extension of the
scan-CUSUM algorithm for a non-constant intensity function, and show that it
achieves asymptotically zero error at the boundary of the zero-error regime. We
illustrate an application of the scan-CUSUM algorithm on multiple sequences
sharing an unknown, non-constant intensity function. We estimate the intensity
function from the change-point profile likelihoods of all sequences and apply
scan-CUSUM on the estimated intensity function.
