Estimating nonlinear regression with and without change-points by the LAD method

摘要

The paper considers the least absolute deviations estimator in a nonlinear parametric regression. The interest of the LAD method is its robustness with respect to other traditional methods when the errors of model contain outliers. First, in the absence of change-points, the convergence rate of estimated parameters is found. For a model with change-points, in the case when the number of jumps is known, the convergence rate and the asymptotic distribution of estimators are obtained. Particularly, it is shown that the change-points estimator converges weakly to the minimizer of given random process. Next, when the number of jumps is unknown, its consistent estimator is proposed, via the modified Schwarz criterion.