In this communication we examine the relationship between maxi–min, Bayes and Nash designs for some hypothesis testing problems. In particular we consider the problem of sample allocation in the standard analysis of variance framework and show that the maxi–min design is also a Bayes solution with respect to the least favourable prior, as well as a solution to a game theoretic problem, which we refer to as a Nash design. In addition, an extension to tests for order is provided.
|Number of pages||28|
|Journal||Electronic Journal of Statistics|
|State||Published - 2020|
Bibliographical noteFunding Information:
The research leading to this paper was conducted (mostly) while the first author was a postdoctoral fellow at the University of Haifa, Israel. The work of the second author is supported by the Israeli Science Foundation Grant No. 456/17 and gratefully acknowledged.
© 2020, Institute of Mathematical Statistics. All rights reserved.
- Bayesian design
- Maxi-min design
- Nash equilibrium
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty