Robustness of Sum of Squared Ranks Test

Abstract

Limiting Pitman efficiencies of the sum of squared ranks test relative to best tests for scale alternative detection are obtained for some specific continuous asymmetrical distributions which have mass confined to the positive axis. In particular the A.R.E. of this test to best tests for gamma distributions is maximized (.9372) when the gamma distribution shape parameter is between five and six. Also this test is an asymptotic locally most powerful rank test for detecting scale alternatives with respect to the distribution formed by doubling the density function of the t distribution with two degrees of freedom over its positive domain.