Qualitative Robustness in Estimation

Mohammed Nasser, Nor Aishah Hamzah, Md. Ashad Alam

Abstract


Qualitative robustness, influence function, and breakdown point are three main concepts to judge an estimator from the viewpoint of robust estimation. It is important as well as interesting to study relation among them. This article attempts to present the concept of qualitative robustness as forwarded by first proponents and its later development. It illustrates intricacies of qualitative robustness and its relation with consistency, and also tries to remove commonly believed misunderstandings about relation between influence function and qualitative robustness citing some examples from literature and providing a new counter-example. At the end it places a useful finite and a simulated version of   qualitative robustness index (QRI). In order to assess the performance of the proposed measures, we have compared fifteen estimators of correlation coefficient using simulated as well as real data sets.


Keywords


Breakdown Point, Influence Function, Qualitative Robustness and Qualitative Robustness Index.

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DOI: http://dx.doi.org/10.18187/pjsor.v8i3.532

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Title

Qualitative Robustness in Estimation

Keywords

Breakdown Point, Influence Function, Qualitative Robustness and Qualitative Robustness Index.

Description

Qualitative robustness, influence function, and breakdown point are three main concepts to judge an estimator from the viewpoint of robust estimation. It is important as well as interesting to study relation among them. This article attempts to present the concept of qualitative robustness as forwarded by first proponents and its later development. It illustrates intricacies of qualitative robustness and its relation with consistency, and also tries to remove commonly believed misunderstandings about relation between influence function and qualitative robustness citing some examples from literature and providing a new counter-example. At the end it places a useful finite and a simulated version of   qualitative robustness index (QRI). In order to assess the performance of the proposed measures, we have compared fifteen estimators of correlation coefficient using simulated as well as real data sets.


Date

2012-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 8. No. 3, 2012



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810