CONFIDENCE SUBSET CONTAINING THE UNKNOWN PEAKS OF AN UMBRELLA ORDERING

Umbrella ordering has received considerable attention in the statistic al Literature during the past 15 years. However, there is still no sol ution to the important problem of estimating the unknown peaks of an u mbrella ordering. This article discusses confidence estimation of the unknown peaks. A random subset of all of the treatments that contains the unknown peaks of an umbrella ordering with any prespecified confid ence level is considered. The proposed order-restricted confidence sub set theory explicitly utilizes the order information and has several a dvantages for umbrella orderings over the usual subset selection theor y. The utility and general applicability of the proposed method is sho wn by its applications in various experimental designs, assuming norma l or other location-scale distributions with known or unknown variance s. Examples based on real data are provided.