One-Sample and Two-Sample Problems

Abstract

In this chapter we consider several one- and two-sample problems in nonparametric statistics. Our approach will have a common thread. We begin by embedding the nonparametric problem into a parametric paradigm. This is then followed by deriving the score test statistic and finding its asymptotic distribution. The construction of the parametric paradigm often involves the use of composite likelihood. It will then be necessary to rely on the use of either linear rank statistics or U-statistics in order to determine the asymptotic distribution of the test statistic. We shall see that the parametric paradigm provides new insights into well-known problems. Starting with the sign test, we show that the parametric paradigm deals easily with the case of ties. We then proceed with the Wilcoxon signed rank statistic and the Wilcoxon rank sum statistic for the two-sample problem.