Upper-Bound or Two-Bound Confidence and Credible Intervals for Restricted Parameter Spaces

• Activity Number: 22
• Type: Contributed
• Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Tonglin Zhang*+
• Companies: Purdue University
• Keywords: frequentist coverage probability ; general scale model ; invariat prior ; monotone likelihood ratio ; two-bound confidence and credible interval ; upper-bound credible and confidence interval

Abstract

Classical confidence sets for the ratio of variance components can degenerate to a single point with positive probability, leaving no allowance for error. Unified and Bayesian methods have been considered to avoids this problem. However, in some cases, the Bayesian credible sets could be always upper-bound intervals, that is the lower bound is always equal to the minimum of parameter domain. This problem exists in many of the Bayesian credible sets for the restriced scale parameter in the general scale model. In this paper, we compare the forms of the three different methods for the confidence or credible intervals for the scale parameter in the general scale model. We will prove that the unified and classical confidence sets are always intervals and not always upper-bound if the density function is monotone likelihood ratio. We will develop the conditions for the Bayesian credible intevals to be always upper-bound or possibly two-bound intervals . We will also show that the coverage probability is always greater than the coverage level for the first case, and the minimum coverage probability is always less than the coverage level for second case.