Constructions of New Classes of One- and Two-Sample Nonparametric Location Tests

Abstract

In this paper, we examine the role of nonparametric test statistics with constructions analogous to those introduced in Mukhopadhyay and Chattopadhyay (Stat Pap 54:827–837 2013) and Mukhopadhyay and Chattopadhyay (Sri Lankan J Appl Stat 15:71–80 2014) in the context of one-sample and two-sample location problems. In the case of a one-sample location problem, we focus on the customary sign test and its appropriate modifications. In the case of a two-sample location problem, we focus on Mann-Whitney test when the population distribution F remains unknown. Using large sample approximations, we propose new versions of tests and compare their performances with those of the customary sign and Mann-Whitney tests. We do so on the basis of asymptotic power, asymptotic efficiency, and robustness. Our present treatment substantially broadens the coverage found in Walsh (Ann Math Stat 17:360–361 1946, Ann Math Stat 20:64–81 1949) and Ylvisaker (J Am Stat Assoc 72:551–556 1977. In summary, we have come up with (i) a test that is more efficient than a sign test, and (ii) a limited optimality of Mann-Whitney test within our class of newly constructed tests.