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二元对称性的非参数检验AI 解读

A conditionally distribution-free test of bivariate symmetry based on the sample distribution function is introduced. The test is shown to be consistent against a wide class of alternatives. In particular, if the underlying bivariate distribution is absolutely continuous, then the test is consistent against all alternatives to the null hypothesis. Power comparisons of the conditional test, a normal theory test devised by Bell and Haller, and the Wilcoxon signed rank test are…

二元对称性的非参数检验AI 解读

A conditionally distribution-free test of bivariate symmetry based on the sample distribution function is introduced. The test is shown to be consistent against a wide class of alternatives. In particular, if the underlying bivariate distribution is absolutely continuous, then the test is consistent against all alternatives to the null hypothesis. Power comparisons of the conditional test, a normal theory test devised by Bell and Haller, and the Wilcoxon signed rank test are…

若干互不相关的非参数检验统计量AI 解读

It is shown that odd translation invariant two sample statistics are uncorrelated with even translation invariant two sample statistics when the distribution function of the combined sample is equally symmetric. This is a generalization of a result of Hogg. It is used to establish conditions under which certain dispersion test statistics (including ones proposed by Lehmann, Mood, Ansari-Bradley-Freund-Barton-David, Klotz and Moses) are uncorrelated with certain location test…

Wilcoxon 两样本检验的两种非参数竞争方法的渐近效率AI 解读

Wilcoxon's signed rank test and a test based on the uniform minimum variance unbiased estimator of P(X 1 + X 2 < Y 1 + Y 2) are considered as competitors of the Mann-Whitney-Wilcoxon (U) test. The criteria used to compare the tests are Bahadur and Pitman efficiency. For pure translation alternatives U is superior, but both tests compare favorably with respect to U for certain contamination alternatives.

Wilcoxon 两样本检验的两种非参数替代方法的渐近效率AI 解读

Wilcoxon's signed rank test and a test based on the uniform minimum variance unbiased estimator of P(X 1 + X 2 < Y 1 + Y 2) are considered as competitors of the Mann-Whitney-Wilcoxon (U) test. The criteria used to compare the tests are Bahadur and Pitman efficiency. For pure translation alternatives U is superior, but both tests compare favorably with respect to U for certain contamination alternatives.