Isotonic M-estimation of location: union-intersection principle and preliminary test versions

In a k (>=2) sample model, isotonic estimators of locations [theta]1, ..., [theta]k take into consideration the prior restraint that [theta]1 <= ... <= [theta]k. Though these estimators are appealling, they are generally biased. The union-intersection (UI-) principle and the theory of M-estimation of location are incorporated in the formulation of some robust, preliminary test, isotonic (M-) estimators of locations. Associated distribution theory of the test statistic and estimator is studied in a systematic manner.