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September, 1987 Qualitative Robustness for Stochastic Processes
Graciela Boente, Ricardo Fraiman, Victor J. Yohai
Ann. Statist. 15(3): 1293-1312 (September, 1987). DOI: 10.1214/aos/1176350506


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.


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Graciela Boente. Ricardo Fraiman. Victor J. Yohai. "Qualitative Robustness for Stochastic Processes." Ann. Statist. 15 (3) 1293 - 1312, September, 1987.


Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0644.62037
MathSciNet: MR902259
Digital Object Identifier: 10.1214/aos/1176350506

Primary: 62F35
Secondary: 62M10

Keywords: autoregressive models , GM-estimators , Qualitative robustness , robust estimation , Stochastic processes

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 3 • September, 1987
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