Abstract
We characterize upper probabilities that are invariant with respect to permutations. A one-to-one relationship is established between generalized upper probabilities, upper probabilities and 2-alternating upper probabilities and certain classes of point functions. In particular, 2-alternating upper probabilities, which are ubiquitous in the statistical robustness literature, are given a simple interpretation. We also show that undominated invariant generalized upper probabilities do not exist.
Research supported by NSF grant DMS-9005858.
Research supported by NSF grant DMS-87-05646 and ONR grant N00014-89-5-1851.
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© 1994 Springer-Verlag New York, Inc.
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Wasserman, L., Kadane, J.B. (1994). Permutation Invariant Upper and Lower Probabilities. In: Gupta, S.S., Berger, J.O. (eds) Statistical Decision Theory and Related Topics V. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2618-5_33
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DOI: https://doi.org/10.1007/978-1-4612-2618-5_33
Publisher Name: Springer, New York, NY
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