One-Term Edgeworth Expansion for Finite Population U-Statistics of Degree Two |
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Authors: | M. Bloznelis F. Götze |
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Affiliation: | (1) Vilnius University, Naugarduko 24, LT-2006 Vilnius, Lithuania. e-mail;(2) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany. e-mail |
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Abstract: | By means of Hoeffding"s decomposition, we represent a finite population U-statistic of degree two by the sum of a linear and a quadratic part. Assuming that the linear part is nondegenerate, we prove the validity of one-term Edgeworth expansion for the distribution function of the statistic under the optimal (minimal) conditions on the linear part and 2 + moment condition on the quadratic part. No condition is imposed on the ratio N / n, where N, respectively n, denotes the sample size respectively the population size. |
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Keywords: | Edgeworth expansion finite population U-statistic |
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