| 关于线性秩统计量的渐近正态性及其收敛速度 |
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| 引用本文： | 李治国. 关于线性秩统计量的渐近正态性及其收敛速度[J]. 应用数学学报, 1998, 0(2) |
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| 作者姓名： | 李治国 |
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| 作者单位： | 中国科学院应用数学研究所!北京，100080 |
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| 摘 要： | 本文讨论线性秩统计量的渐近正态性的条件及其收敛速度．推广了Hajek关于线性秩统计量收敛于正态分布的条件的重要定理，并得出了一个较易验证的充分条件．对于一般形式的计分函数，在一定条件下得出了相应线性秩统计量收敛于正态分布的速度．
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| 关 键 词： | 线性秩统计量 渐近正态性 收敛速度 |
ON THE ASYMPTOTIC NORMALITY OF LINEAR RANK STATISTICS AND ITS CONVERGENCE RATE |
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| LI ZHIGUO. ON THE ASYMPTOTIC NORMALITY OF LINEAR RANK STATISTICS AND ITS CONVERGENCE RATE[J]. Acta Mathematicae Applicatae Sinica, 1998, 0(2) |
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| Authors: | LI ZHIGUO |
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| Abstract: | The asymptotic normality of linear rank statistics under less restricted conditions than that of Hajek is established in this paper. Meanwhile, a condition that is easy to be tested in practice is established to be used for more practical purposes. Some examples are given to illustrate the effectiveness of this condition. Then the author discussed the convergence rate of linear rank statistics. Various rates under various conditions are given here, which are better than the existing ones. |
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| Keywords: | Linear rank statistics asymptotic normality convergence rate |
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