  The problem to establish not only the asymptotic distribution results for
statistical estimators but also the moment convergence of the estimators has
been recognized as an important issue in advanced theories of statistics. One
of the main goals of this paper is to present a metod to derive the moment
convergence of $Z$-estimators as it has been done for $M$-estimators. Another
goal of this paper is to develop a general, unified approach, based on some
partial estimation functions which we call "$Z$-process", to the change point
problems for ergodic models as well as some models where the Fisher information
matrix is random and inhomogeneous in time. Applications to some diffusion
process models and Cox's regression model are also discussed.
