Orthogonal multiple contrast test for testing monotone on the average

Dykstra and Robertson [1983. On testing monotone tendencies. J. Amer. Statist. Assoc. 78, 342-350] proposed the likelihood ratio tests for testing "decreasing on the average" which is closely related to the "starshaped ordering" discussed in Shaked [1979. Estimation of starshaped sequences of Poisson and normal means. Ann. Statist. 7, 729-741]. We propose an orthogonal multiple contrast test which is easily implemented and has good and fairly uniform power. It can also be used to construct simultaneous confidence intervals.