Speaker: Chaoyu Yu, Graduate Student, UW Biostatistics
Abstract: Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of groups, their actual coverage rate for a given group will be above or below the nominal rate, depending on the value of the group mean. Alternatively, a coverage rate that is constant as a function of a group’s mean can be simply achieved by using a standard t-interval, based on data only from that group. The standard t-interval, however, fails to share information across the groups and is therefore not adaptive to easily obtained information about the distribution of group-specific means. We construct confidence intervals that have a constant frequentist coverage rate and that make use of information about across-group heterogeneity, resulting in constant coverage intervals that are narrower than standard t-intervals on average across groups.