Symmetric, coherent, Choquet capacities

Annals of Statistics

Volumn 24, Issue 3, 1996, Pages 1250-1264

  Kadane, Joseph B ^a   Wasserman, Larry ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

2 alternating capacities; Bayesian robustness; Choquet capacities; Equimeasurability; Lower probabilities; Majorization

Indexed keywords

EID: 0030489102     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032526967     Document Type: Article

References (34)

1. ANGER, B. and LEMBCKE, J. (1985). Infinitely subadditive capacities as upper envelopes of measures. Z. Wahrsch. Verw. Gebiete 68 403-414.
2. ARMSTRONG, T. (1990). Comonotonicity, simplical subdivision of cubes and non-linear expected utility via Choquet integrals. Technical Report, Dept. Math. Statist., Univ. Maryland.
3. BEDNARSKI, T. (1981). On solutions of minimax test problems for special capacities. Z. Wahrsch. Verw. Gebiete 58 397-405.
4. BEDNARSKI, T. (1982). Binary experiments, minimax tests and 2-alternating capacities. Ann. Statist. 10 226-232
5. BERGER, J. (1984). The robust Bayesian viewpoint (with discussion). In Robustness in Bayesian Statistics (J. Kadane, ed.). North-Holland, Amsterdam.
6. BERGER, J. (1990). Robust Bayesian analysis: sensitivity to the prior. J. Statist. Plann. Inference 25 303-328.
7. BUJA, A. (1986). On the Huber-Strassen theorem. Probab. Theory Related Fields 73 367-384.
8. CHOQUET, G. (1969). Lectures on Analysis 2. Benjamin/Cummings, Reading, MA.
9. DEMPSTER, A. P. (1967). Upper and lower probabilities induced from a multivalued mapping. Ann. Math. Statist. 38 325-339.
10. DEMPSTER, A. P. (1968). A generalization of Bayesian inference (with discussion). J. Roy. Statist. Soc. Ser. B 30 205-247.
11. DENNEBERG, D. (1994). Non-additive Measure and Integral. Kluwer, Dordrecht.
12. DEROBERTIS, L. and HARTIGAN, J. A. (1981). Bayesian inference using intervals of measures. Ann. Statist. 9 235-244.
13. FINE, T. (1988). Lower probability models for uncertainty and nondeterministic processes. J. Statist. Plann. Inference 20 389-411.
14. FORTINI, S. and RUGGERI, F. (1994). Concentration functions and Bayesian robustness. J. Statist. Plann. Inference 40 205-220.
15. GILBOA, I. (1987). Expected utility theory with purely subjective non-additive probabilities. J. Math. Econom. 16 65-88.
16. HUBER, P. J. (1973). The use of Choquet capacities in statistics. Bull. Inst. Internat. Statist. 45 181-191.
17. HUBER, P. J. (1981). Robust Statistics. Wiley, New York.
18. HUBER, P. J. and STRASSEN, V. (1973). Minimax tests and the Neyman-Pearson lemma for capacities. Ann. Statist. 1 251-263.
19. LAVINE, M. (1991a). Sensitivity in Bayesian statistics: the prior and the likelihood. J. Amer. Statist. Assoc. 86 396-399.
20. LAVINE, M. (1991b). An approach to robust Bayesian analysis for multidimensional parameter spaces. J. Amer. Statist. Assoc. 86 400-403.
21. MARSHALL, A. W. and OLKIN, I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.
22. PAPAMARCOU, A. and FINE, T. (1986). A note on undominated lower probability. Ann. Probab. 14 710-723.
23. RYFF, J. (1963). On the representation of doubly stochastic operators. Pacific J. Math. 13 1379-1386.
24. 1-functions under doubly stochastic transformations. Trans. Amer. Math. Soc. 117 92-100.
25. RYFF, J. (1967). On Muirhead's theorem. Pacific J. Math. 21 567-576.
26. RYFF, J. (1970). Measure preserving transformations and rearrangements. J. Math. Anal. Appl. 31 449-458.
27. SADROLHEFAZI and FINE, T. (1994). Finite-dimensional distributions and tail behavior in stationary interval-valued probability models. Ann. Statist. 22 1840-1870.
28. SCHMEIDLER, D. (1989). Subjective probability and expected utility without additivity. Econometrica 67 571-587.
29. SHAPLEY, L. (1971). Cores of convex games. Internat. J. Game Theory 1 11-26.
30. SMITH, C. A. B. (1961). Consistency in statistical inference and decision (with discussion). J. Roy. Statist. Soc. Ser. B 23 1-37.
31. TALAGRAND, M. (1978). Capacités invariantes extrémales. Ann. Inst. Fourier (Grenoble) 28 79-146.
32. WALLEY, P. (1991). Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London.
33. WASSERMAN, L. A. and KADANE, J. (1990). Bayes' theorem for Choquet capacities. Ann. Statist. 18 1328-1339.
34. WASSERMAN, L. A. and KADANE, J. (1992). Symmetric upper probabilities. Ann. Statist. 20 1720-1736.