Consistent estimation in generalized broken-line regression

A change-point model is considered where the canonical parameter of an exponential family drifts from its control value at an unknown time and changes according to a broken-line regression. Necessary and sufficient conditions are obtained for the existence of consistent change-point estimators. When sufficient conditions are met, it is shown that the maximum likelihood estimator of the change point is consistent, unlike the classical abrupt change-point models. Results are extended to the case of nonlinear trends and nonequidistant observations. © 2003 Elsevier B.V. All rights reserved.