On Bayesian credible sets in restricted parameter space problems and lower bounds for frequentist coverage
Abstract
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1\alpha$ and frequentist coverage probability bounded below by $\frac{1\alpha}{1+\alpha}$. In cases where the underlying pivotal distribution is symmetric, the findings represent extensions with respect to the specification of the credible set achieved through the choice of a {\it spending function}, and include Marchand and Strawderman's HPD procedure result. For nonsymmetric cases, the determination of a such a class of Bayesian credible sets fills a gap in the literature and includes an "equaltails" modification of the HPD procedure. Several examples are presented demonstrating wide applicability.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 arXiv:
 arXiv:1208.0028
 Bibcode:
 2012arXiv1208.0028M
 Keywords:

 Mathematics  Statistics Theory;
 62C10;
 62F15;
 62F25;
 62F30
 EPrint:
 This is an expanded version of an earlier post