GENERALIZED MEDIAN TEST FOR TWO-SAMPLE LOCATION PROBLEM USING MULTIPLE TYPE-II CENSORED DATA B. S. Biradar Department of Studies in Statistics, University of Mysore, Mysore - 570 006, India. E-mail: biradarbs@statistics.uni-mysore.ac.in Abstract : In this article, median test for complete data is generalized to multiple Type-II censored data for the two-sample location problem. Since, the scores generating function associated with generalized median (GM) test statistic has a finite number of jump discontinuities, a modified version of the Dupac and Hajek (1969) theorem is used to establish its asymptotic normality under fixed location alternatives. The effect of censoring on the asymptotic efficiency (ARE) is studied. It is found that as long as the median of the data is available any particular case of multiple Type-II censoring has no effect on the ARE of the GM test. There is a gain in efficiency due to middle censoring when the underlying distribution is normal, logistic and extreme value distributions. This suggests that in this case, it is possible to improve the efficiency of GM test by discarding suitable portions of the data. Key words : Multiple Type-II censored data, Generalized Median Test, Asymptotic relative efficiency, Loss of efficiency. Received December 26, 2014 Revised February 14, 2015 Accepted March 06, 2015 1. Introduction Ordered data arise naturally in many branches of applied statistics, including, among others, survival analysis and life testing in biomedical sciences, duration analysis in economics and reliability theory in engineering. Sometimes even the recorded observations may be lost by accident or negligence, or may be discarded if found unreliable. Such situations give rise to multiply censored samples. Here, we consider the multiple Type–II censored data, where some sets of observations including some extremely small and extremely large observations from the combined ordered sample are censored. The parametric estimation in the case of multiple censored data has received considerable attention [Balakrishnan and Cohen (1991), Balakrishnan et al. (1995a, b), David and Nagaraja (2003) and Fernandez (2006)]. However, in the non- parametric setting, not much work is done when the data are multiple Type II censored except couple of paper by Mehrotra et al. (1977) and Chikkagoudar and Biradar (2010). Mehrotra et al. (1977) have obtained the locally most powerful (LMP) rank test for two- sample problem with general parametric alternative, when the data are triple Type-II censored. Recently, Chikkagoudar and Biradar (2010) have obtained asymptotic distribution of LMP rank tests and studied the effect of censoring on the asymptotic efficiency of the two-sample tests for location and scale alternatives when the combined ordered samples from different underlying distributions are censored using triple and lower ordered Type-II censoring schemes. The main objective of this paper is to adopt median test for the above testing problem with multiple Type- II censored data and then to study the extent of loss in the Pitman asymptotic relative efficiency (ARE) due to the censoring. In section 2, we derive LMP rank for two-sample location problem based on multiple Type- II censored data. In section 3, the median test is modified to the case of multiple Type-II censored data and its properties are studied. The effect of censoring schemes on asymptotic efficiency of GM test is discussed in Section 4. 2. Rank Tests using Multiple Type-II Censored Data for two Sample Location Problem Let X 1 , ..., X m and Y 1 , ..., Y n be two independent random samples from two absolutely continuous distribution functions F(x) and G(x), respectively, with Int. J. Agricult. Stat. Sci. Vol. 11, No. 2, pp. .....-....., 2015 ISSN : 0973-1903 ORIGINAL ARTICLE