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不连续分布下 Smirnov 型两样本秩检验的分布AI 解读

Summary An important area of application for rank tests occurs when there are ties in the data which may happen when the observations are drawn from a discrete population or are grouped. The standard theory for the two-sample Smirnov test as to whether two samples have been drawn from the same population assumes continuous distributions in which case ties only arise with probability zero. The null distribution of the test statistic for large sample sizes is obtained here for…

由连续分段线性函数生成的秩检验AI 解读

The two-sample problem of testing against location shift is fundamental to much of the theory of rank tests. Generally testing and estimation is carried out with a fixed (non-random) set of scores for the ranks. However Beran (1974), following ideas of Stein and Hajek, developed a notable class of adaptive estimators. When used in testing, these give asymptotically efficient tests, regardless of the underlying distribution. These ideas are used here to focus attention upon…

两种 Mann–Whitney 型秩检验AI 解读

Summary Two Mann-Whitney type rank tests are introduced and their test statistics related to the test statistics of the Smirnov tests. The null distributions of the test statistics are studied both for small sample sizes and in terms of limiting distributions. A lower bound for the power of these tests is obtained. Monte Carlo methods are employed to assess the power of the tests against competitors; the Mann-Whitney type tests perform well. Bahadur efficiency is also used…

Bahadur效率意义下线性秩检验的不可容许性AI 解读

Hajek (1974) has shown that in the two-sample problem the best exact slope for a test of randomness against any particular member of a large class of alternative hypotheses is attained by a linear rank test. Here a new class of two-sample rank tests is constructed, and it is shown that for each linear test there exists a test within the new class which is always at least as efficient in terms of exact Bahadur efficiency irrespective of which alternative hypothesis, is…

两样本秩检验的影响曲线AI 解读

Summary An influence curve for two-sample linear rank tests is introduced. This influence curve can be viewed as a derivative of the limiting power and reflects the stability of the power to deviations from the assumed hypothesis testing model. It can also be interpreted in terms of the limit in probability of the test statistic and then it indicates the effect that small changes in the observations have upon the test statistic. The stability properties of several tests are…

圆周数据 Mann–Whitney 型统计量的小样本分布AI 解读

The union-intersection method of test construction can be used to derive from the Mann-Whitney rank test a test statistic for testing whether two samples of observations from circular distributions come from the same population. The null distribution of this test statistic will be investigated here. The approach followed is to use the principle of inclusion-exclusion to obtain an expression for the number of partitions of a positive integer which satisfy certain conditions.…

关于潜根回归中乘子的一个注记AI 解读

Summary A recent treatment of multiple regression involves the use of Lagrange multipliers. These multipliers are explicitly characterized in this note as partial covariances.