Nonparametric multiple sample scale testing using U-statistics

Abstract

Testing of equality of scale parameters is one of the fundamental problems in Statistics and is useful in many fields such as agriculture, engineering, experimental methods and dose level testing. In this paper, we propose a new class of nonparametric tests, to test whether the scale parameters of all the populations are equal, or there is an umbrella ordering in the scale parameters. The proposed test is based on weighted linear combination of two-sample U-statistics. The optimal choice of weights is determined so that proposed tests have maximum efficiency. The comparison of proposed test with respect to existing tests is made in terms of Pitman asymptotic relative efficiency. A numerical example is provided for illustrative purpose. Power of the proposed test is also assessed using Monte Carlo simulation study.