On powerful distributional tests based on sample spacings
On powerful distributional tests based on sample spacings
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基于样本间距的强大分布测试
DOI：
10.1016/0047-259x(86)90027-8
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发表时间：
1986
影响因子：
1.6
通讯作者：
P. Hall
中科院分区：
文献类型：
--
作者：
P. Hall
本文致力于基于m-间隔和函数的一致性检验，其中m随着样本量n的增加而发散到无穷大。结果表明，如果m的发散速度比n1 2的发散速度慢，则常用的求和函数可以检测到与−1 4相距较远的备选方案。如果m比n 1 2发散得更快，那么这个结果就失败了，在这种情况下，必须修改统计量。文中还考虑了m n→ϱ，0<；ϱ<；1的情形，并且证明了当且仅当ϱ无理时，该检验对局部和固定备选方案具有足够的能力。
This paper is devoted to tests for uniformity based on sum-functions of m-spacings, where m diverges to infinity as the sample size, n, increases. It is shown that if m diverges at a slower rate than n 1 2 then the commonly used sum-function will detect alternatives distant (mn)− 1 4 from the uniform. This result fails if m diverges more quickly than n 1 2, and in that situation the statistic must be modified. The case where m n→ ϱ, 0< ϱ< 1, is also considered, and it is shown that the test has adequate power against local and fixed alternatives if and only if ϱ is irrational.