Abstract
We prove the sharp bound for the expected spread upon opinions of n≥2 experts, who have access to different information sources represented by different σ-fields. Using symmetrization argument and direct combinatorial optimization we derive an explicit optimizer. Our results may turn out to be helpful not only for probabilists, but also for statisticians and economists.
Highlights
The purpose of this paper is to establish a certain sharp maximal estimate for dependent random variables which stems from applications in statistics and information theory
Opinions on an event A ∈ F will be expressed as random variables
We apply an appropriate symmetrization and reduce the problem of calculating the left-hand side of (1.2) to the analysis of the simpler expression sup E max1≤i≤n Xi, where the supremum is taken over all coherent vectors satisfying
Summary
The purpose of this paper is to establish a certain sharp maximal estimate for dependent random variables which stems from applications in statistics and information theory. We apply an appropriate symmetrization and reduce the problem of calculating the left-hand side of (1.2) to the analysis of the simpler expression sup E max1≤i≤n Xi, where the supremum is taken over all coherent vectors satisfying. After several steps, this allows us to express the supremum as the extremal value of a certain function of one variable, which in turn can be computed explicitly. Our approach was inspired by the paper [3] by Burdzy and Pal: in that article, a related problem for coherent vectors was studied with the use of a certain discretization and subsequent combinatorial reductions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
