Open Journal of Statistics, 2014, 4, 70-74 Published Online February 2014 (http://www.scirp.org/journal/ojs ) http://dx.doi.org/10.4236/ojs.2014.41007 OPEN ACCESS OJS Tests for Two-Sample Location Problem Based on Subsample Quantiles Parameshwar V. Pandit 1 , Savitha Kumari 2 , S. B. Javali 3 1 Department of Statistics, Bangalore University, Bangalor, India 2 Department of Statistics, SDM College, Ujire, India 3 Department of Public Health Dentistry, SDM College of Dental Sciences and Hospital, Dharwad, India Email: panditpv12@gmail.com , savi_rrao@yahoo.co.in , javalimanju@rediffmail.com Received November 6, 2013; revised December 6, 2013; accepted December 13, 2013 Copyright © 2014 Parameshwar V. Pandit et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property Parameshwar V. Pandit et al. All Copyright © 2014 are guarded by law and by SCIRP as a guardian. ABSTRACT This paper presents a new class of test procedures for two-sample location problem based on subsample quan- tiles. The class includes Mann-Whitney test as a special case. The asymptotic normality of the class of tests pro- posed is established. The asymptotic relative performance of the proposed class of test with respect to the optim- al member of Xie and Priebe (2000) is studied in terms of Pitman efficiency for various underlying distributions. KEYWORDS U-Statistic; Class of Tests; Two-Sample Location Problem; Asymptotic Normality; Pitman ARE; Subsample Quantiles 1. Introduction Two-sample location problem is one of the extensively studied problems in the literature. There are many non- parametric 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 the median test is particularly effective for heavy tailed symmetric distributions, the normal score and Mann-Whitney tests are relatively even handed and reasonably effective for moderately heavy tailed bell shaped distributions. 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]. While Shetty and Govindarajulu [6] and Shetty and Bhat [7] based their tests on subsample medians which tend to emphasize the centre of the un- derlying 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. For example, in consonance with the efficiency results noted in the last paragraph, Shetty and Govindarajulu [6] test performs on one hand better than the Mann- Whitney test for heavy-tailed distributions, while performing better than the median test for light-tailed distribu- tions on the other. Deshpande and Kochar [2] test, on the other hand, being sensitive to light-tailed distributions, performs substantially better than Mann-Whitney test for such underlying distributions and some what better for normal, while maintaining reasonable level of efficiency under heavy-tailed distributions. Stephenson and Ghosh [3] and Ahmad [8] tests are also relatively more sensitive than the Mann-Whitney test but less than the Deshpande and Kochar [2] test to the light-tailed distributions. Recently, Xie and Priebe [9] proposed a genera-