A note on the generalization of Rosenbaum's test for two-sample scale problem

Article type: Research Article

Authors: Joshi, Venkatesh B.^a | Shetty, Ishwar D.^b

Affiliations: [a] JSS Institute of Economic, Research, PRC, Vidygiri, Dharwad-580004, Karnataka state, India. E-mail: [email protected] | [b] Department of statistics, Karnatak University, Dharwad-580003, Karnataka state, India. E-mail: [email protected]

Abstract: Rosenbaum [12] proposed a distribution-free test for the two-sample scale problem based on a number of X-sample observations lying between the extremes of the Y-sample observations. We propose a distribution-free test for the two-sample scale problem; this test is resistant to possible outliers in both samples and generalizes the tests due to Rosenbaum [12] as well as a test due to Shetty and Bhat [7]. The performance of the test is evaluated in terms of Pitman's asymptotic relative efficiency. An alternative expression in terms of ranks of ordered X-sample observations in the joint ranking of X and Y-sample observations is given to facilitate the computation of the test statistic and tabulate the upper cutoff points of the exact null distribution of the test statistic.

Keywords: Two-sample scale problem, Pitman ARE, distribution-free, cutoff points

DOI: 10.3233/MAS-2008-3106

Journal: Model Assisted Statistics and Applications, vol. 3, no. 1, pp. 59-69, 2008