Asymptotic Theory for some Families of Two-Sample Nonparametric Statistics.

摘要

Let X(1),...,X(m-1), and Y(1),...,Y(n) be independent random samples from two continuous distribution functions F and G. We wish to test H(0):F=G. Let X'(1)< or = ...< or =X'(m-1) be the ordered X-observations. Denote by S(k) the number of Y-observations falling between X'(k-1) and X'(k). Asymptotic distribution theory and limiting efficiencies are studied for best statistics of the form sum of h(s(k)) symmetrically in the sets S(k) and sum of h(s(k)) which are not symmetric in the sets S(k), where h(.) and the set h(k(.)) are real valued functions satisfying some simple regularity conditions. (Author)