CONFIDENCE-INTERVAL ESTIMATION SUBJECT TO ORDER RESTRICTIONS

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.