Edgeworth Expansion for U -statistics under Minimal Conditions by Bing-yi Jing
نویسنده
چکیده
It is well known that Gn(x) converges to the standard normal distribution function, (x), provided Eh(X1,X2) <∞ [see Hoeffding (1948)]. In fact, this moment condition can further be reduced to Eg(X1) <∞ and E|h(X1,X2)|4/3 <∞; see Remark 4.2.4 of Koroljuk and Borovskich [(1994), page 131]. In recent years, there has been considerable interest in obtaining rates of convergence in the asymptotic normality for U -statistics, for instance, by Grams and Serfling (1973), Bickel (1974) and Chan and Wierman (1977). A sharper Berry–Esseen bound was given by Callaert and Janssen (1978), which states that
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