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 θ 1 is n 1/2 -consistent. The asymptotic distribution of n 1/2 (θ ^ 1n − θ 0 1 ) 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.