INVESTIGADORES
BOENTE BOENTE Graciela Lina
artículos
Título:
Qualitative robustness for stochastic processes
Autor/es:
BOENTE, GRACIELA; FRAIMAN, RICARDO; YOHAI, VÍCTOR
Revista:
ANNALS OF STATISTICS, THE
Editorial:
Institute of Mathematical Statistics
Referencias:
Año: 1987 vol. 15 p. 1293 - 1312
ISSN:
0090-5364
Resumen:
In this paper we generalize Hampel´s concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non-i.i.d. observations, defining appropriate metrics between samples. We also present a different approach to qualitative robustness which formalizes the notion of resistance. We give two definitions based on this approach: strong and weak resistance. We show that for estimating a finite dimensional real parameter, $pi$-robustness is equivalent to weak resistance and, in the i.i.d. case, is also equivalent to strong resistance. Finally, we prove the strong resistance of a class of estimators which includes common GM-estimates for linear models and autoregressive processes.