Asymptotic properties of M-estimators based on estimating equations and censored data in semi-parametric models with multiple change points

Abstract

Statistical models with multiple change points in presence of censored data are used in many fields; however, the theoretical properties of M-estimators of such models have received relatively little attention. The main purpose of the present work is to investigate the asymptotic properties of M-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, in the setting of a known number of change points. Consistency of the M-estimators of the change points is established and the rate of convergence is determined. The asymptotic normality of the M-estimators of the parameters of the within-segment distributions is established. Since the approaches used in the complete data models are not easily extended to multiple change-point models in the presence of censoring, we have used some general results of Kaplan-Meier integrals. We investigate the performance of the methodology for small samples through a simulation study.