A test against an umbrella ordered alternative

Singh, P. and Liu, W. (2006) A test against an umbrella ordered alternative. Computational Statistics and Data Analysis, 51 (3), 1957-1964. (doi:10.1016/j.csda.2005.12.010).

Abstract

Consider k(k3) independent populations ?1,…,?k such that cumulative distribution function (cdf) of an observation from population ?i is Fi(x)=F[(x-?i)/?i], a member of general location scale family, where F(.) is any absolutely continuous cdf, ?i(-?<?i<?) is the location parameter and ?i(?i>0) is the scale parameter, i=1,…,k. It is assumed that scale parameters ?is satisfy the umbrella ordering ?1?h?k with at least one strict inequality, where 1hk is given. When h is equal to 1 or k the umbrella ordering is just the simple ordering. Gill and Dhawan [1999. A one-sided test for testing homogeneity of scale parameters against ordered alternative. Comm. Statist. Theory Methods 28(10), 2417–2439] considered the problem of testing the null hypothesis H0:?1==?k against the simple ordering alternative, and provided some critical points by using simulation technique. In this paper a one-sided test for testing null hypothesis H0 against the umbrella ordered alternative Ha:?1?h?k with at least one strict inequality is proposed. A recursive method to compute the exact critical points for the test procedure is proposed and selected tables of critical points for exponential probability model are provided. The proposed test is inverted to obtain a set of one-sided simultaneous confidence intervals for all the ordered pairwise ratios ?j/?i for 1i<jh and for hj<ik, which enable the experimenter to infer which ?is are different and by how much when H0 is rejected. Applications of the proposed test procedure to normal and inverse Guassian distributions are also discussed.

This record has no associated files available for download.

Contributors

Author: W. Liu

Download statistics