Maximum likelihood estimator in a two-phase nonlinear random regression model

Summury We consider a two-phase random design nonlinear regression model, the regression function is discontinuous at the change-point. The errors ∊ are arbitrary, with E(∊) = 0 and E(∊2) < ∞. We prove that Koul and Qian’s results [12] for linear regression still hold true for the nonlinear case. Thus the maximum likelihood estimator r^n of the change-point r is n-consistent and the estimator θ^1n of the regression parameters θ1 is n1/2-consistent. The asymptotic distribution of n1/2(θ^1n − θ01) is Gaussian and n(r^n − r) converges to the left end point of the maximizing interval with respect to the change point. The likelihood process is asymptotically equivalent to a compound Poisson process.