Abstract
ABSTRACTWe study Poisson confidence procedures that potentially lead to short confidence intervals, investigating the class of all minimal cardinality procedures. We consider how length minimization should be properly defined, and show that Casella and Robert's (1989) criterion for comparing Poisson confidence procedures leads to a contradiction. We provide an alternative criterion for comparing length performance, identify the unique length optimal minimal cardinality procedure by this criterion, and propose a modification that eliminates an important drawback it possesses. We focus on procedures whose coverage never falls below the nominal level and discuss the case in which the nominal level represents mean coverage.
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