Constructing Confidence Regions of Optimal Expected Size
Chad M. Schafer and Philip B. Stark
We present a Monte Carlo method for approximating the minimax expected
size (MES) confidence set for a parameter known to belong to a compact set.
Size refers to the measure of the confidence set; the measure
can be indexed by the true parameter value, which allows the confidence
procedure to be tailored for specific scientific goals. As the number of
iterations increases, the Monte Carlo estimator converges to the
-minimax procedure, where
is a polytope of priors.
The algorithm exploits Bayes/minimax duality by searching for the
-least favorable prior. A Fortran-90 implementation of the algorithm
for both serial and parallel computers is available. We apply the method
to estimate parameters of the primordial universe from observations of the
cosmic microwave background radiation.