应用数学学报 1981, Vol. 4 Issue (4): 342-355    DOI:
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Chen Xi-ru
University of Science and Technology of China
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Abstract： This paper considers the linear permutation statistics Lυ generated from two sequences Aυ={aυ1,…,aυp} and Bυ={aυ1,…,aυNp}.We show that when Aυ and Bυ both satisfy the condition W then (normalization of Lυ) converges in law to the Standard Normal with a rate not lower than O(Nυ-(1/b)+ε) for any ε>0.We get even better results in cases where Lυ is produced by some two-sample tests.Further,in case Aυ and Bυ both satisfy the condition N,We determine the class of all possible limit distributions of .Also it is shown that,when one of Aυ and Bυ satisfies W and the other satisfies N,and no further conditions are imposed,then the convergence of to the Standard Normal can be arbitrarily slow.
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 引用本文: 陈希孺. 线性置换统计量的两个问题[J]. 应用数学学报, 1981, 4(4): 342-355. Chen Xi-ru. TWO PROBLEMS OF LINEAR PERMUTATION STATISTICS[J]. Acta Mathematicae Applicatae Sinica, 1981, 4(4): 342-355.

  中国科学院数学研究所代数组,关于有限域1F4上循环矩阵的周期,尚未发表.  H.Crater,Mathematical Methods of Statiatics,Princeton Univ.Press,1946.  R.M.Dudley,Convergence of Baire Measures,S'tudia Math.,27(1966),251-268.
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