Data-Driven Tests for Trend

This article proposes a new nonparametric test for the ordered alternatives problem in the k-sample setting for null hypothesis of lack of trend. This article further elaborates upon and extends the results of Ledwina and Wy?upek (2012a Ledwina , T. , Wy?upek , G. ( 2012a ). Two-sample test against one-sided alternatives . Scand. J. Statist. 39 : 358 – 381 .Crossref], Web of Science ®] , Google Scholar]) obtained for k = 2. Simulations show that the new test has high and stable power and is able to control the Type I error to satisfactory extent, thus solving the problem posed in Terpstra and Magel (2003 Terpstra , J. T. , Magel , R. C. ( 2003 ). A new nonparametric test for the ordered alternative problem . J. Nonparametr. Statist. 15 : 289 – 301 .Taylor & Francis Online], Web of Science ®] , Google Scholar]). Our theoretical results say that asymptotic errors of both kinds do not exceed significance level, thus implying that the test is asymptotically unbiased.