The Annals of Statistics

Qualitative Robustness for Stochastic Processes

Graciela Boente, Ricardo Fraiman, and Victor J. Yohai

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 15, Number 3 (1987), 1293-1312.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350506

Digital Object Identifier
doi:10.1214/aos/1176350506

Mathematical Reviews number (MathSciNet)
MR902259

Zentralblatt MATH identifier
0644.62037

JSTOR
links.jstor.org

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Qualitative robustness robust estimation GM-estimators stochastic processes autoregressive models

Citation

Boente, Graciela; Fraiman, Ricardo; Yohai, Victor J. Qualitative Robustness for Stochastic Processes. Ann. Statist. 15 (1987), no. 3, 1293--1312. doi:10.1214/aos/1176350506. https://projecteuclid.org/euclid.aos/1176350506


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