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Let U_n be a U-statistic with symmetric kernel h(x,y) such that Eh(X_1,X_2)=θ and Var E[h(X_1,X_2)-θ|X_j]>0.Let f(x) be a function defined on R and f″ be bounded.If f(θ) is the parameterof interest,a natural estimator is f(U_n).It is known that the distribution function of z_n=(n~(1/2){Jf(U_n)-f(θ)})/(S_n~*) converges to the standard normal distribution Φ(x) as n→∞,where Jf(U_n) isthe jackknife estimator of f(U_n),and S_n~(*2) is the jackknife estimator of the asymptotic variance ofn~(1/2) Jf(U_n).It is of theoretical value to study the rate of the normal approximation of the statistic.In this paper,assuming the existence of fourth moment of h(X_1,X_2),we show that(?)|P{z_n≤x}-Φ(x)|=O(n~(-1/2)log n).This improves the earlier results of Cheng(1981).  相似文献
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In this paper, we propose jackknife only for a particular class of non-symmetric statistics, which is incomplete U-statistics of significance in practice. We find that if we deal with incomplele U-statistics using a slightly modified jackknife, then Tu-key's conjecture will be true, and the consistent estimator of asymptotic variance is given. Thus we obtain an approximate confidence interval for reguluar function g (θ).  相似文献
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In this note some recurrence relations for the dimensions of the spline spaces on so called 0-stars are presented. The work of this author is supported by the Alexander von Humboldt Foundation This paper is completed at Free Univ. Berlin, Inst. of Math., Arnimallee 2–6, 1000 Berlin 33, Germany  相似文献
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