  Consider a statistical problem where a set of parameters are of interest to a
researcher. Then multiple confidence intervals can be constructed to infer the
set of parameters simultaneously. The constructed multiple confidence intervals
are the realization of a multiple interval estimator (MIE), the main focus of
this study. In particular, a thresholding approach is introduced to improve the
performance of the MIE. The developed thresholds require additional
information, so a prior distribution is assumed for this purpose. The MIE
procedure is then evaluated by two performance measures: a global coverage
probability and a global expected content, which are averages with respect to
the prior distribution. The procedure defined by the performance measures will
be called a Bayes MIE with thresholding (BMIE Thres). In this study, a
normal-normal model is utilized to build up the BMIE Thres for a set of
location parameters. Then, the behaviors of BMIE Thres are investigated in
terms of the performance measures, which approach those of the corresponding
z-based MIE as the thresholding parameter, C, goes to infinity. In addition, an
optimization procedure is introduced to achieve the best thresholding parameter
C. For illustrations, in-season baseball batting average data and leukemia gene
expression data are used to demonstrate the procedure for the known and unknown
standard deviations situations, respectively. In the ensuing simulations, the
target parameters are generated from different true generating distributions to
consider the misspecified prior situation. The simulation also involves Bayes
credible MIEs, and the effectiveness among the different MIEs are compared with
respect to the performance measures. In general, the thresholding procedure
helps to achieve a meaningful reduction in the global expected content while
maintaining a nominal level of the global coverage probability.
