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U-统计量的精致渐近性   总被引：1，自引：1，他引：0       下载免费PDF全文

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<正> 关于 U-统计量的渐近展开,至今尚无较为理想的结果.最近的工作是 Callaert,Jan-ssen 和 Veraverbeke.假设 X_1,X_2,…是具有共同的分布函数 F(x)的独立随机变量序列,定义 U-统计量  相似文献

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Let X_1,X_2,…,X_n be independent random variables. Define a U-statistic by U_n(?)~(-1)sum from 1≤i≤j≤n (h(X_i,X_j), where h(x,y) is a symmetric function of two variables x,y and that Eh(X_i,X_j)=0(i≠j, i,j=1,2,…,n). Write g_j(X_i)=E(h(x_i,x_j)|x_i),g(X_1)=1/n-1 sum from j=1 j≠i to n g_j(X_i) We give the following two theorem: Theorem 1 Suppore that  相似文献

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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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《代数通讯》2013,41(4):1065-1072
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We show that, for generic bihomogeneous polynomials, the determinant of the matrix of moving planes is irreducible.  相似文献

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《代数通讯》2013,41(12):5639-5650

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