Far East Journal of Theoretical Statistics © 2017 Pushpa Publishing House, Allahabad, India http://www.pphmj.com http://dx.doi.org/10.17654/TS053010047 Volume 53, Number 1, 2017, Pages 47-61 ISSN: 0972-0863 Received: July 26, 2016; Revised: August 9, 2016; Accepted: December 13, 2016 2010 Mathematics Subject Classification: 62G10. Keywords and phrases: asymptotic relative efficiency, subsample extremes, special two- sample location problem, U-statistics. SOME CLASSES OF NONPARAMETRIC TESTS FOR SPECIAL TWO-SAMPLE LOCATION PROBLEM BASED ON SUBSAMPLE EXTREMES Parameshwar V. Pandit 1 and Deepa R. Acharya 2 1 Department of Statistics Bangalore University Bengaluru 560 056, India e-mail: panditpv@bub.ernet.in; panditpv12@gmail.com 2 Department of Statistics Government Science College Bengaluru 560 001, India e-mail: deeparacharya@yahoo.co.in Abstract The special two-sample location problem is an important problem which is useful in comparing the performance of two measuring instruments. The problem of comparing the performances of two packing machines in which one machine may underfill the packets and the other may overfill the packets on an average, fits into special two- sample location setup wherein one wishes to test for the point of symmetry versus an appropriate alternative. The only test available in the literature to the best of our knowledge is the class of tests due to Shetty and Umarani [13] which is based on U-statistics. In this paper, two classes of test statistics are proposed which are based on extremes of subsamples. The performances of the proposed classes of tests are