SOME QUICK SIGN TESTS FOR TREND IN LOCATION AND DISPERSION
SOME QUICK SIGN TESTS FOR TREND IN LOCATION AND DISPERSION
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DOI：
10.1093/biomet/42.1-2.80
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发表时间：
1955-01-01
期刊：
影响因子：
2.7
通讯作者：
STUART, A
中科院分区：
文献类型：
--
作者：
COX, DR;STUART, A
许多无分布检验被设计来检验一系列iNV观测的随机性假设，即假设N个独立随机变量具有相同的连续分布函数。其中，秩相关检验是对正态趋势替代方案最有效的检验，但其他检验在计算速度和简单性很重要的情况下也有一定的用处。本文讨论了一类简单的符号检验，首先将其作为位置趋势检验。从渐近相对效率（大样本中局部功率的测量）的角度来看，发现最佳检验，并且似乎这些检验中最好的可能优于文献中考虑的其他简单检验，尽管它们的效率当然低于秩相关检验。在正常情况下，类似的测试可用于分散趋势和这些的效率。并与基于极大似然估计的检验进行了比较。最后，我们补充了一些关于序列符号检验的注释。对这个理论不感兴趣的读者应该看看？？10，11和14，其中有测试和数值示例的简要说明。
Many distribution-free tests have been devised to test the hypothesis of randomness of a series of iNV observations, ie the hypothesis that N independent random variables have the same continuous distribution function. Of these, the rank correlation tests are the most efficient tests agaiinst normal trend alternatives, but others are of some use in situations where speed and simplicity of computation are important. In this paper, we discuss a class of simple sign tests, considered first as tests against trend in location. Optimum tests are found from the standpoint of asymptotic relative efficiency (a measure of local power in large samples), and it appears that the best of these tests may be preferred to the other simple tests considered in the literature, although they are, of course, less efficient than the rank correlation tests. Similar tests are available for trend in dispersion, and the efficiency of these, in the normal situation. is investigated and compared with the test based on the maximum-likelihood estimator. Finally, we add a few remarks on sequential sign tests. Readers not interested in the theory should look at?? 10, 11 and 14, where there are brief statements of the tests and numerical examples.