An Automatic Test for the Umbrella Alternatives
提出一种新的非参数检验方法，用于检测数据是否呈现伞形模式，并控制检验的第一类错误不超过显著性水平，模拟显示优于现有方法。
Abstract The paper proposes a new test for detecting the umbrella pattern under a general non‐parametric scheme. The alternative asserts that the umbrella ordering holds while the hypothesis is its complement. The main focus is put on controlling the power function of the test outside the alternative. As a result, the asymptotic error of the first kind of the constructed solution is smaller than or equal to the fixed significance level α on the whole set where the umbrella ordering does not hold. Also, under finite sample sizes, this error is controlled to a satisfactory extent. A simulation study shows, among other things, that the new test improves upon the solution widely recommended in the literature of the subject. A routine, written in R, is attached as the Supporting Information file.