| U-统计量的精致渐近性 |
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| 引用本文： | 严继高,苏淳.U-统计量的精致渐近性[J].数学学报,2007,50(3):517-526. |
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| 作者姓名： | 严继高 苏淳 |
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| 作者单位： | [1]中国科学技术大学统计与金融系,合肥230026 [2]苏州大学数学科学学院,苏州215006 |
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| 基金项目： | 国家自然科学基金(10371117,10271087) |
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| 摘 要： | 设{X_n．n≥1}是一非退化的i．i．d．随机变量序列,U_n是以二维Borel可测对称函数h(x,y)为核函数的U-统计量．记U_n=2/(n(n-1))Σ_≤i≤j≤nh(X_i,X_j)．本文分别在核函数h(x,y)只有4/3阶矩或4/3+δ,0＜δ≤1的情况下,对非常广泛的一类权函数(x)与边界函数b(x)得到了如下关于U-统计量U_n的精致渐近性:不仅使得已有的结果成为我们的特况,还大大降低了其中的矩条件．
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| 关 键 词： | U-统计量 精致渐近性 矩条件 |
| 文章编号： | 0583-1431（2007）03--0517-10 |
| 收稿时间： | 2005-4-20 |
| 修稿时间： | 2005-04-20 |
Precise Asymptotics of U-Statistics |
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| Ji Gao YAN ,Chun SU.Precise Asymptotics of U-Statistics[J].Acta Mathematica Sinica,2007,50(3):517-526. |
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| Authors: | Ji Gao YAN Chun SU |
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| Institution: | Ji Gao YAN Department of Statistics & Finance,University of Science and Technology of China,Hefei 230026,P.R.China Department of Mathematics,Soochow University,Suzhou 215006,P.R.China Chun SU Department of Statistics & Finance,University of Science and Technology of China,Hefei 230026,P.R.China |
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| Abstract: | Let {X,X_n,n≥1} be non-degenerate i.i.d.random variables,define a U-statistics U_n=2/(n(n-1))∑_≤j≤j≤nh(X_i,X_j),where h(x,y) is a 2-dimensional Borel measurable and symmetric kernel function.Under the condition of E|h(X_1,X_2)|~(4/3) or E|h(X_1,X_2)|~((4/3)+δ),0＜δ≤1 separately,for a very extensive weighted functionφ(x) and a boundary function b(x),we discuss the precise asymptotics of U_n as follows: where a is an appropriate non-negative number.It not only makes the known results on this subject as the special case of our results,but also reduces their moment conditions. |
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| Keywords: | U-statistics precise asymptotics moment conditions |
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