Abstract: | Two classes of estimators of a location parameter ø0 are proposed, based on a nonnegative functional H1* of the pair (D1øN, GøN), where and where FN is the sample distribution function. The estimators of the first class are defined as a value of ø minimizing H1*; the estimators of the second class are linearized versions of those of the first. The asymptotic distribution of the estimators is derived, and it is shown that the Kolmogorov-Smirnov statistic, the signed linear rank statistics, and the Cramérvon Mises statistics are special cases of such functionals H1*;. These estimators are closely related to the estimators of a shift in the two-sample case, proposed and studied by Boulanger in B2 (pp. 271–284). |