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Minimax Tests and the Neyman-Pearson Lemma for Capacities
Open accessAbstract
Robust test problems between two approximately known simple hypotheses can be formalized as minimax test problems between two composite hypotheses. We show that if the composite hypotheses can be described in terms of alternating capacities of order 2 (in the sense of Choquet), then the minimax tests are ordinary Neyman-Pearson tests between a fixed representative pair of simple hypotheses; moreover, the condition is in a certain sense also necessary. All the neighborhoods customarily used to formalized approximate knowledge happen to have this particular structure.
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Cited by
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Kassam, S. A., & Poor, H. V. (1985) · Proceedings of the IEEE · doi:10.1109/proc.1985.13167 · Cited by 815
Additive representations of non-additive measures and the choquet integral
Gilboa, I., & Schmeidler, D. (1994) · Annals of Operations Research · doi:10.1007/bf02032160 · Cited by 280
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Donoho, D. L., & Liu, R. C. (1991) · The Annals of Statistics · doi:10.1214/aos/1176348114 · Cited by 261
Robust covariance and scatter matrix estimation under Huber’s contamination model
Chen, M., Gao, C., & Ren, Z. (2018) · The Annals of Statistics · doi:10.1214/17-aos1607 · Cited by 146
Metadata
- Authors
- Huber, P. J., & Strassen, V.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1973-03-01
- Volume
- 1
- Issue
- 2
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2010161926
- Cited by
- 499
- References
- 0
- FWCI
- 1.84
- Type
- journal article
- Language
- en
- Open access
- bronze
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