Distribution-Free Tests for Two-Sample Location Problems Based on Subsamples

Nonparametric tests for location problems have received much attention in the literature. Many nonparametric tests have been proposed for one, two and several samples location problems. In this paper a class of test statistics is proposed for two sample location problem when the underlying distributions of the samples are symmetric. The class of test statistics proposed is linear combination of U-statistics whose kernel is based on subsamples extrema. The members of the new class are shown to be asymptotically normal. The performance of the proposed class of tests is evaluated using Pitman Asymptotic Relative Efficiency. It is observed that the members of the proposed class of tests are better than the existing tests in the literature

A Class of Nonparametric Tests for the Two-Sample Location Problem

The two-sample location problem is one of the fundamental problems encountered in Statistics. In many applications of Statistics, two-sample problems arise in such a way as to lead naturally to the formulations of the null hypothesis to the effect that the two samples come from identical populations. A class of nonparametric test statistics is proposed for two-sample location problem based on U-statistic with the kernel depending on a constant ’a’ when the underlying distribution is symmetric. The optimal choice of ’a’ for different underlying distributions is determined. An alternative expression for the class of test statistics is established. Pitman asymptotic relative efficiencies indicate that the proposed class of test statistics does well in comparison with many of the test statistics available in the literature. The small sample performance is also studied through Monte-Carlo Simulation techniqu

SOME CLASSES OF NONPARAMETRIC TESTS FOR SPECIAL TWO-SAMPLE LOCATION PROBLEM BASED ON SUBSAMPLE EXTREMES

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 twosample 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 ar

A Class of Nonparametric Tests for the Two-Sample Location Problem

The two-sample location problem is one of the fundamental problems encountered in Statistics. In many applications of Statistics, two-sample problems arise in such a way as to lead naturally to the formulations of the null hypothesis to the effect that the two samples come from identical populations. A class of nonparametric test statistics is proposed for two-sample location problem based on U-statistic with the kernel depending on a constant ’a’ when the underlying distribution is symmetric. The optimal choice of ’a’ for different underlying distributions is determined. An alternative expression for the class of test statistics is established. Pitman asymptotic relative efficiencies indicate that the proposed class of test statistics does well in comparison with many of the test statistics available in the literature. The small sample performance is also studied through Monte-Carlo Simulation technique