This article deals with the construction of confidence intervals when
the components of the location parameter mu of the random variable X,
which is elliptically symmetrically distributed, are subject to order
restrictions. Several domination results are proved by studying the de
rivative of the coverage probability of the confidence intervals cente
red at the improved point estimators. Consequently, we strengthen the
previously known results regarding the simple ordering and obtain seve
ral new results for other general forms of order restrictions, includi
ng the simple tree ordering, the umbrella ordering, the simple and the
double loop ordering and some combination of these. These domination
results are obtained under the assumption that SIGMA is a diagonal mat
rix. When SIGMA is nondiagonal, some new intervals are introduced whic
h dominate the standard intervals centered at the unrestricted maximum
likelihood estimator for various types of order restrictions. Similar
results are obtained for scale parameters as well. Contrary to the lo
cation problems, in case of the scale parameters satisfying the simple
ordering we find that the restricted maximum likelihood estimator of
the largest parameter fails to universally dominate the unrestricted m
aximum likelihood estimator. A similar negative result is noted for si
mple tree order restriction.