Asymptotics of maximum likelihood estimator in a two-phase linear regression model

This paper considers two-phase random design linear regression models with arbitrary error densities and where the regression function has a fixed jump at the true change-point. It obtains the consistency and the limiting distributions of maximum likelihood estimators of the underlying parameters in these models. The left end point of the maximizing interval with respect to the change point, herein called the maximum likelihood estimator (r) over cap (n) of the change-point parameter r, is shown to be n-consistent and the underlying likelihood process, as a process in the standardized change-point parameter, is shown to converge weakly to a compound Poisson process. This process obtains maximum over a bounded interval and n((r) over cap (n) - r) converges weakly to the left end point of this interval. These results are different from those available in the literature for the case of the two-phase linear regression models when jump sizes tend to zero as n tends to infinity. (C) 2002 Elsevier Science B.V. All rights reserved.