Abstract
“Prophet theory” quantifies the price a statistician has to pay for his lack of information in stochastic sequences. In a recent paper, Schmitz (1991) gave a game-theoretical interpretation of this situation and he formulated in particular a minimax conjecture for the difference case. In this note we prove that conjecture and, moreover, present minimax ran domized stopping times (minimax procedures for the statistician).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chow, Y.S., Robbins, H. and Siegmund, D. (1971): Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.
Irle, A. (1990). Minimax stopping times and games of stopping. 11th Prague Conference (forthcoming).
Kertz, R. (1986). Prophet problems in optimal stopping: results, techniques and variations. Preprint Georgia Institute of Technology.
Rauhut, B., N. Schmitz, E.-W. Zachow (1979). Spieltheorie. Teubner, Stuttgart
Schmitz, N. (1991). Games against a prophet. Contemporary Mathematics (forthcoming).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gödde, M. Statistical games against a prophet-proof of a minimax conjecture. Statistical Papers 32, 75–81 (1991). https://doi.org/10.1007/BF02925482
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02925482