Asymptotic Theory for some Families of Two-Sample Nonparametric Statistics.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Let X1,...,Xm-1, and Y1,...,Yn be independent random samples from two continuous distribution functions F and G. We wish to test H0FG. Let X1 or ... or Xm-1 be the ordered X-observations. Denote by Sk the number of Y-observations falling between Xk-1 and Xk. Asymptotic distribution theory and limiting efficiencies are studied for best statistics of the form sum of hsk symmetrically in the sets Sk and sum of hsk which are not symmetric in the sets Sk, where h. and the set hk. are real valued functions satisfying some simple regularity conditions. Author
- Statistics and Probability