Abstract
AbstractTwo 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).
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