Stability ofL 1-approximations and robustness of least module estimates

The paper is concerned with the robustness properties of least module (LM) estimates of regression parameters depending on the stability properties of L₁-norm approximations. The conditions of stability for L₁-approximations are obtained in linear, nonlinear, continuous, and discrete cases. The breakdown points of LM estimates and their upper bounds are derived in the linear case of approximation by algebraic and trigonometric polynomials, and in the nonlinear case of approximation by exponentials. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.