Nonparametric tests for comparing umbrella pattern treatment effects with a control in a one-way layout were studied in Chen and Wolfe (1993). In this paper a recursive formula for deriving the isotonic regression which is useful for statistical inference under the umbrella pattern restriction is given. An alternative multiple test procedure is then considered for the setting where the peak of the umbrella is known. The results of a Monte Carlo power study are presented.
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION