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Minimax vs. Bayes Prediction

Published online by Cambridge University Press:  27 July 2009

D. Blackwell
D. Blackwell
Affiliation:
Department of Statistics, University of California, Berkeley, Berkeley, California 94720
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Extract

Let x = (x1, x2, …) be an infinite sequence of 0's and 1's, initially unknown to you. On day n = 1,2,…, you observe hn = (x1, …, xn–1), the first n – 1 terms of the sequence, and must predict xn. What is a good prediction method, and how well can you do?

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 1 , January 1995 , pp. 53 - 58
Copyright
Copyright © Cambridge University Press 1995

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References

1.Blackwell, D. (1956). An analog of the minimax theorem for vector payoffs. Pacific Journal of Mathematics 6: 1–8.Google Scholar
2.Lerche, H.R. & Sarkar, J. (1994). The Blackwell prediction algorithm for infinite 0-1 sequences, and a generalization. In Gupta, S.S. & Berger, J.O. (eds.), Statistical decision theory and related topics. New York: Springer, pp. 503–511.Google Scholar
3.Stout, W.F. (1974). Almost sure convergence. New York: Academic Press.Google Scholar