Estimation: The Two-Sample Shift Model

Abstract

When in Chapter 8 we compared the two-sample t-test to the Wilcoxon test, we briefly mentioned the so-called shift model according to which Y-observations are shifted by an unknown amountδrelative to X-observations as in Figure 9.1.The two-sample shift model represents a generalization of the classical two-sample model underlying the two-sample t-test, whereX-and Y-observations are assumed to be normally distributed with the same standard deviation. In the general two-sample shift model, we only assume that one population may have been shifted relative to the other population, but we do not make any assumptions about the shape of the population distribution. This latter fact is often cited as justification for using the term nonparametric in connection with two-sample shift problems, even though the problems frequently involve explicitly the parameterδ.Indeed, in this chapter we discuss how to estimate the shift parameterδ.