The unbalanced ranked-set sample sign test

Abstract

This paper is concerned with the sign test under unbalanced ranked-set sampling (URSS), which constitutes a generalization of the usual ranked-set sampling (RSS). The null distribution properties of the URSS sign test are discussed. Accordingly, a URSS sign test optimized on the basis of the asymptotic relative efficiency criterion is introduced. The proposed test is compared with the RSS analog by means of both asymptotic relative efficiency properties as well as small-sample Monte Carlo power simulations. The results strongly encourage the use of the optimized URSS sign test.

Keywords:

• Nonparametric test
• Order statistics
• Unbalanced ranked-set data