Asymptotic Properties of Maximum
Likelihood Estimators in Models with Multiple Change Points
Models with
multiple change points are used in many fields; however, the theoretical
properties 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 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 development of new tools for analyzing the likelihood
function in a multiple change-point model.