  Models with multiple change points are used in many fields; however, the
theoretical properties of maximum likelihood estimators of such models have
received relatively little attention. The goal of this paper is to establish
the asymptotic properties of maximum likelihood estimators of the parameters of
a multiple change-point model for a general class of models in which the form
of the distribution can change from segment to segment and in which, possibly,
there are parameters that are common to all segments. Consistency of the
maximum likelihood estimators of the change points is established and the rate
of convergence is determined; the asymptotic distribution of the maximum
likelihood estimators of the parameters of the within-segment distributions is
also derived. Since the approach used in single change-point models is not
easily extended to multiple change-point models, these results require the
introduction of those tools for analyzing the likelihood function in a multiple
change-point model.
