Change-Point Estimation as a Nonlinear Regression Problem

Abstract

A special class of change-point models, where the change is defined as a shift of observations means, is considered. We show that such models can be transformed into a nonlinear regression problem. It is proven that M-estimators can localize the change point, and at the same time, consistently estimate the unknown parameters characterizing the change behavior. For a special class of continuous models we prove an asymptotic normality of M-estimators simultaneously estimating the change-point and the related parameters.

AMS Classifications:

• 62F12
• 62F35

Keywords:

• Change-point estimation
• M-estimates