Abstract
This paper presents a new class of test procedures for two-sample location problem based on subsample quantiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests proposed is established. The asymptotic relative performance of the proposed class of test with respect to the optimal member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions.
Highlights
Two-sample location problem is one of the extensively studied problems in the literature
For example there is a whole class of locality asymptotically most powerful linear rank tests for each specified distribution F, which included the well known Mann-Whitney, normal score and median tests among many others ([1], Ch-III, 1.1)
During the last decade or so, new classes of tests based on the so called subsample approach have been proposed for the above problem, notable among them being Deshpande and Kochar [2], Stephenson and Gosh [3], Shetty and Govindarajulu [6], Shetty and Bhat [7] and Ahmad [8]
Summary
Two-sample location problem is one of the extensively studied problems in the literature. There are many nonparametric tests available in literature for the above problem, their relative efficiency and suitability depending on the nature of the (unknown) underlying distribution F For this problem, for example there is a whole class of locality asymptotically most powerful (distribution free) linear rank tests for each specified distribution F, which included the well known Mann-Whitney, normal score and median tests among many others ([1], Ch-III, 1.1). While Shetty and Govindarajulu [6] and Shetty and Bhat [7] based their tests on subsample medians which tend to emphasize the centre of the underlying distributions, the other two are based on statistics involving subsample extrema with the object of gaining more information from the tails of sampled distributions The results of these papers demonstrate that the subsample approach, applied selectively, does help to improve upon the efficiency performance of the tests mentioned in the preceding paragraph in an overall sense. Xie and Priebe [9] proposed a genera-
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