ABSTRACT
This chapter develops a general, unified approach based on a partial sum process of estimating function, which we call “Z-process”, to some change point problems in mathematical statistics. The asymptotic representation theorems for Z-estimators and the functional CLTs for martingales, both of which were established in the previous chapters, will play the key roles to analyze our test statistic defined based on the Z-process. The limit distribution of the test statistic under the null hypothesis that there is no change point is the supremum of standard Brownian bridges. The consistency of the test under the alternative is also proved in a general way.
Some applications to Markov chain models and diffusion process models are discussed.
