Nonparametric Confidence Intervals for a Shift Parameter

E. L. Lehmann
1963 The Annals of Mathematical Statistics  
Exact expressions and large-sample approximations are given for the nonparametric confidence intervals for a shift parameter ~, which are obtained from the two-sample Wilcoxon test. These intervals are shown to have the same asymptotic efficiency relative to the standard confidence intervals for ~ as the Wilcoxon test has relative to Student's t-test. As a consequence of this result, a constant multiple of the length of the nonparametric intervals is shown to be a consistent estimator of the
more » ... ntity 1/ ff (x) dx. Let X1, · · · , Xm and Y1, · · · , Yn be independent observations from dis-
doi:10.1214/aoms/1177703882 fatcat:52xsknuisffctn5ecfpqdykzae