On Distribution-free Tests for One-sample Location Problem Based on Subsample Exterma

Abstract

One-sample location problem is one of fundamental problems in nonparametric inference.
Wilcoxon signed rank test is the most popular test for location when the distribution of the
underlying sample is from a symmetric continuous distribution. In this paper, we propose a
distribution-free class of statistics for one-sample location problem based on U-statistic whose
kernel depends on subsample extrema. The asymptotic distribution of the proposed class of test
statistics is established using U-statistic theory. The performance of few members of the class is
evaluated in terms of Pitman asymptotic relative efficiency relative to the Wilcoxon signed rank
test, test proposed by Mehra, Prasad and Rao (1990), Shetty and Pandit (2000) and Rattihalli and
Raghunath (2012). It is observed that the members of the proposed class of tests are better than
the tests mentioned above for heavy and light tailed distributions.