Qualitative Robustness for General Stochastic Processes

Abreviated Title: Qualitative Robustness SUMMARY In this paper we generalize Hampel's definition of robustness and IT-robustness of a sequence of estimators to the case of non i.i.d. stochastic processes, using appropriate metrics on the space of finite and infinite dimensional samples. We also present a different approach to qualitative robust-ness based on uniform insensitivity of the sequence of estimators when the sample is affected by round-off errors or by a small fraction of outliers. We give two definitions based on this approach: strong and weak pointwise robustness. We show that for estimating a finite dimensional real parameter, IT-robustness is equivalent to weak pointwise robustness and at least in the i.i.d. case is also equivalent to strong pointwise robustness. Finally we show that the continuity condition given by Papantoni-Kazakos and Gray is sufficient for strong pointwise robustness. This implies the strong point-wise robustness of GM-estimates for autoregressive models. 1.mators stochastic processes and-2-Qualitative robustness for general stochastic processes