The Annals of Probability

Robustness of Estimators on Stationary Observations

P. Papantoni-Kazakos and Robert M. Gray

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Abstract

Hampel's general qualitative definition of robustness of sequences of estimators on memoryless observation processes is generalized to stationary ergodic processes by substituting the generalized Ornstein (or $\bar{\phi}$) distance for the marginal Prohorov distance as the measure of "closeness" of observations. More general sequences of estimators are also allowed. The approach yields results analogous to those of Hampel for the more general case considered, often provides strict generalizations of Hampel's results, and in some cases yields simpler proofs.

Article information

Source
Ann. Probab., Volume 7, Number 6 (1979), 989-1002.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994892

Digital Object Identifier
doi:10.1214/aop/1176994892

Mathematical Reviews number (MathSciNet)
MR548893

Zentralblatt MATH identifier
0426.62021

JSTOR
links.jstor.org

Subjects
Primary: 62G35: Robustness
Secondary: 60B05: Probability measures on topological spaces 60H99: None of the above, but in this section

Keywords
Robust estimation stationary data ergodicity stochastic distance measures

Citation

Papantoni-Kazakos, P.; Gray, Robert M. Robustness of Estimators on Stationary Observations. Ann. Probab. 7 (1979), no. 6, 989--1002. doi:10.1214/aop/1176994892. https://projecteuclid.org/euclid.aop/1176994892


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