Bivariate Nonparametric Tests for the One-Sample Location Problem

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 tests
• Bivariate signed rank tests
• Nonparametric tests
• Invariance under linear transformations