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A General Qualitative Definition of Robustness
Open accessAbstract
Two very closely related definitions of robustness of a sequence of estimators are given which take into account the types of deviations from parametric models that occur in practice. These definitions utilize the properties of the Prokhorov distance between probability distributions. It is proved that weak $^\ast$-continuous functionals on the space of probability distributions define robust sequences of estimators (in either sense). The concept of the "breakdown point" of a sequence of estimators is defined, and some examples are given.
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Cites
Robust estimation of a location parameter
Huber, P. J. (1964) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177703732 · Cited by 7,228
Cited by
High Breakdown-Point and High Efficiency Robust Estimates for Regression
Yohai, V. J. (1987) · The Annals of Statistics · doi:10.1214/aos/1176350366 · Cited by 1,644
Principles and procedures of exploratory data analysis.
Behrens, J. T. (1997) · Psychological Methods · doi:10.1037/1082-989x.2.2.131 · Cited by 465
A Survey of Multidimensional Medians
Small, C. G. (1990) · International Statistical Review / Revue Internationale de Statistique · doi:10.2307/1403809 · Cited by 393
Robust Estimation of Dispersion Matrices and Principal Components
Devlin, S. J., Gnanadesikan, R., & Kettenring, J. R. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477654 · Cited by 391
Robust statistics in data analysis — A review
Daszykowski, M., Kaczmarek, K., Vander Heyden, Y., & Walczak, B. (2007) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2006.06.016 · Cited by 331
Metadata
- Authors
- Hampel, F. R.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1971-12
- Volume
- 42
- Issue
- 6
- Pages
- 1887-1896
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2095225664
- Cited by
- 1,002
- References
- 1
- FWCI
- 2.74
- Type
- journal article
- Language
- en
- Open access
- diamond
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