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SB-Robustness of Estimators

In: Recent Advances in Robust Statistics: Theory and Applications

Author

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  • Arnab Kumar Laha

    (Indian Institute of Management Ahmedabad, Production and Quantitative Methods)

  • A. C. Pravida Raja

    (Indian Institute of Management Ahmedabad)

Abstract

Examining the SB-robustness of estimators becomes important in situations where the underlying family of distributions has bounded support or bounded parameter space. Such situations occur routinely when dealing with circular data and statistical quality control. In this paper, we first discuss SB-robustness of estimators in the circular data set-up and review some of the recently obtained results in this regard. Later in the paper, we examine the SB-robustness of some of the commonly used performance measures of control charts which are widely used for control of manufacturing processes. It is shown that for a mean control chart, the False Alarm Probability (FAP), the Average Sample Number when the process is in-control ( $$ASN_0$$ ), the No-Signal Probability (NSP), and the Average Sample Number when the process is out-of-control ( $$ASN_1$$ ) are all SB-robust at the family of all normal distributions with bounded mean and standard deviation. We also show that the above-mentioned performance measures are not SB-robust at the larger family of normal distributions with unbounded mean and standard deviation.

Suggested Citation

  • Arnab Kumar Laha & A. C. Pravida Raja, 2016. "SB-Robustness of Estimators," Springer Books, in: Claudio Agostinelli & Ayanendranath Basu & Peter Filzmoser & Diganta Mukherjee (ed.), Recent Advances in Robust Statistics: Theory and Applications, pages 115-130, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-3643-6_6
    DOI: 10.1007/978-81-322-3643-6_6
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