  Change point analysis has applications in a wide variety of fields. The
general problem concerns the inference of a change in distribution for a set of
time-ordered observations. Sequential detection is an online version in which
new data is continually arriving and is analyzed adaptively. We are concerned
with the related, but distinct, offline version, in which retrospective
analysis of an entire sequence is performed. For a set of multivariate
observations of arbitrary dimension, we consider nonparametric estimation of
both the number of change points and the positions at which they occur. We do
not make any assumptions regarding the nature of the change in distribution or
any distribution assumptions beyond the existence of the alpha-th absolute
moment, for some alpha in (0,2). Estimation is based on hierarchical clustering
and we propose both divisive and agglomerative algorithms. The divisive method
is shown to provide consistent estimates of both the number and location of
change points under standard regularity assumptions. We compare the proposed
approach with competing methods in a simulation study. Methods from cluster
analysis are applied to assess performance and to allow simple comparisons of
location estimates, even when the estimated number differs. We conclude with
applications in genetics, finance and spatio-temporal analysis.
