Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1147817 | Journal of Statistical Planning and Inference | 2010 | 8 Pages |
Abstract
We determine a credible set A that is the “best” with respect to the variation of the prior distribution in a neighborhood Î of the starting prior Ï0(θ). Among the class of sets with credibility γ under Ï0, the “optimally robust” set will be the one which maximizes the minimum probability of including θ as the prior varies over Î. This procedure is also Î-minimax with respect to the risk function, probability of non-inclusion. We find the optimally robust credible set for three neighborhood classes Î, the ε-contamination class, the density ratio class and the density bounded class. A consequence of this investigation is that the maximum likelihood set is seen to be an optimal credible set from a robustness perspective.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Sudip Bose,