 
Summary: Statistics & Decisions 19, 137 (2001)
c R. Oldenbourg Verlag, M¨unchen 2001
Minimax estimators of the coverage probability
of the impermissible error for a location family
Miguel A. Arcones
Received: Month1 99, 2003; Accepted: Month2 99, 2004
Summary: We consider estimation for a multivariate location family. Between all confidence
regions with volume less than a fixed value L, we find the equivariant confidence region with the
biggest coverage probability. This region maximizes the infimum of the coverage probability over
all confidence regions with volume less than L. As an application, we find an estimator of a location
parameter with the property that minimizes the supremum of the probability that the error of the
estimation exceeds a fixed constant. We also find a confidence region and an estimator having the
previous properties, but based on the maximum likelihood estimator. In the one dimensional case,
we find the Bahadur slope of the two obtained estimators. We show that except for certain families
of distributions, the estimator based on the whole sample is superior to the estimator based upon
the m.l.e. Hence, we get that m.l.e.'s are not asymptotically sufficient.
February 6, 2008
1 Introduction
We consider the estimation of the parameter indexing a family {f(·, ) : } of
p.d.f.'s, where is a Borel subset of Rd
