An algorithm for calculating Γ-minimax decision rules under generalized moment conditions

Annals of Statistics

Volumn 29, Issue 4, 2001, Pages 1094-1116

  Noubiap, Roger Fandom ^a   Seidel, Wilfried ^a  

^a HELMUT SCHMIDT UNIVERSITY   (Germany)

Author keywords

minimax decision rules; Bayesian robustness; Experimental design; Minimax problems; Monotone decision problems; Semi infinite programming

Indexed keywords

EID: 0035732137     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1013699995     Document Type: Article

References (22)

1. BERGER, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer, New York.
2. BERGER, J. O. (1990). Robust Bayesian analysis: sensitivity to the prior. J. Statist. Plann. Inference 25 303-328.
3. BETRÒ, B., RUGGERI, F. and MȨCZARSKI, M. (1994). Robust Bayesian analysis under generalized moment conditions. J. Statist. Plann. Inference 41 257-266.
4. BETRÒ, B. and GUGLIELMI, A. (1996). Numerical robust bayesian analysis under generalized moment conditions (with discussion) In Bayesian Robustness (J. O. Berger, B. Betrò, E. Moreno, L. R. Pericchi, F. Ruggeri, G. Salinetti and L. Wasserman, eds.) 3-19. IMS, Hayward, CA.
5. DALL'AGLIO, M. and SALINETTI, G. (1994). Bayesian robustness, moment problem and semi-infinite linear programming, Poster Presented at the Fifth Valencia Meeting, Alicante (Spain), 5-9 June 1994.
6. GOBERNA, M. A. and LÓPEZ, M. A. (1998). Linear Semi-Infinite Optimization. Wiley, Chichester.
7. GUSTAFSON, S. A. (1973). Nonlinear systems in semi-infinite programming. In Numerical Solution of Systems of Nonlinear Algebraic Equations (G. D. Byrne and C. A. Hall, eds.) 63-99. Academic Press, New York.
8. HETTICH, R. and KORTANEK, K. O. (1993). Semi-infinite programming: theory, methods and applications. SIAM Rev. 35 380-429.
9. HETTICH, R. and ZENCKE, P. (1982). Numerische Methoden der Approximation und semi-infiniten Optimierung. Teubner, Stuttgart.
10. KEMPERMAN, J. H. B. (1987). Geometry of the moment problem. In Moments in Mathematics (H. J. Landau, ed.) 37 1-15. Amer. Math. Soc., Providence, RI.
11. KRUMBHOLZ, W. (1982). Die Bestimmung einfacher Attributprüfpläne unter Berücksichtigung von unvollständiger Vorinformation. Allgemeines Stat. Archiv 66 240-253.
12. LAI, H. C. and WU, S. Y. (1992). On linear semi-infinite programming problems, an algorithm. Numer. Funct. Anal. Optim. 13 287-304.
13. NELDER, J. A. and MEAD, R. (1965). A Simplex method for function minimization. Comput. J. 7 308-313.
14. PARKINSON, J. M. and HUTCHINSON, D. (1972). An investigation into the efficiency of variants of the simplex method. In Numerical Methods for Nonlinear Optimization (F. A. Lootsma, ed.) 115-135. Academic Press, New York.
15. REEMTSEN, R. and GÖRNER, S. (1998). Numerical methods for semi-infinite programming: a survey. In Semi-Infinite Programming (R. Reemtsen, and J. J. Rückmann, eds.) 195-275. Kluwer, Boston.
16. REEMTSEN, R. and RÜCKMANN, J. J. (eds.) (1998). Semi-Infinite Programming. Kluwer, Boston.
17. ROLEFF, K. (1979). A stable multiple exchange algorithm for linear SIP, Lecture Notes in Control and Inform. Sci. 15 83-96. Springer, Berlin.
18. SCHMITZ, N. (1992). Optimal Sequentially Planned Decision Procedures. Lecture Notes in Statist. 79. Springer, Berlin.
19. SITTER, R. R. (1992). Robust designs for binary data. Biometrics 48 1145-1155.
20. SMITH, J. E. (1995). Generalized Chebychev inequalities: theory and application. In Decision Analysis, Operations Research 43 807-825.
21. THYREGOD, P. (1974). Bayesian single sampling acceptance plans for finite lot sizes. J. Roy. Statist. Soc. Ser. B 36 305-319.
22. WINKLER, G. (1988). Extreme points of moment sets. Math. Oper. Res. 13 581-587.