Distribution-free tests for umbrella alternatives in a randomized block design

Abstract

A distribution-free test for umbrella alternatives in a randomized block design is proposed and the asymptotic properties of the proposed test statistic, the asymptotic relative efficiencies (AREs) of the proposed test statistic with respect to the Hettmansperger and Norton's statistic and the Puri's parametric method are investigated. With 4 blocks and 5 treatments, when the peak point is 3, from a small sample Monte Carlo study, the empirical powers of the proposed statistic, Hettmansperger and Norton's statistic and Puri's statistic are compared. Throughout the simulation results, the proposed test statistic compared to the Puri's statistic is efficient for heavy tailed distributions .

Keywords:

• Distribution-free test
• umbrella alternatives
• asymptotic relative efficiency
• empirical powers