Bivariate Nonparametric Tests for the One-Sample Location Problem
本文改进了已有的双变量符号检验和符号秩检验，使其具有线性变换下的不变性，并通过蒙特卡洛研究证明新方法在小样本下的效率与功效优于原方法。
Abstract Abstract Many nonparametric competitors to Hotelling's T2 test lack T 2's property of invariance under linear transformations. Such tests have power and efficiency that depend on the direction of shift and the covariance matrix of the alternative distribution. This article modifies a previously proposed bivariate sign test and signed rank test to overcome this difficulty. Asymptotic results and a Monte Carlo study indicate that the efficiency and small-sample power of the new procedures compare favorably to those of the original tests. An example illustrates the application of the new procedures. Key Words: Bivariate sign testsBivariate signed rank testsNonparametric testsInvariance under linear transformations