The construction of confidence regions for parameter vectors is a difficult
problem in the nonparametric setting, particularly when the sample size is not
large. The bootstrap has shown promise in solving this problem, but empirical
evidence often indicates that some bootstrap methods have difficulty in
maintaining the correct coverage probability, while other methods may be
unstable, often resulting in very large confidence regions. One way to improve
the performance of a bootstrap confidence region is to restrict the shape of
the region in such a way that the error term of an expansion is as small an
order as possible. To some extent, this can be achieved by using the bootstrap
to construct an ellipsoidal confidence region. This paper studies the effect of
using the smoothed and iterated bootstrap methods to construct an ellipsoidal
confidence region for a parameter vector. The smoothed estimate is based on a
multivariate kernel density estimator. This paper establishes a bandwidth
matrix for the smoothed bootstrap procedure that reduces the asymptotic
coverage error of the bootstrap percentile method ellipsoidal confidence
region. We also provide an analytical adjustment to the nominal level to reduce
the computational cost of the iterated bootstrap method. Simulations
demonstrate that the methods can be successfully applied in practice