  An important problem in statistics is the construction of confidence regions
for unknown parameters. In most cases, asymptotic distribution theory is used
to construct confidence regions, so any coverage probability claims only hold
approximately, for large samples. This paper describes a new approach, using
random sets, which allows users to construct exact confidence regions without
appeal to asymptotic theory. In particular, if the user-specified random set
satisfies a certain validity property, confidence regions obtained by
thresholding the induced data-dependent plausibility function are shown to have
the desired coverage probability.
