Download e-book for iPad: Acta Numerica 1997: Volume 6 by Arieh Iserles

By Arieh Iserles

ISBN-10: 0521591066

ISBN-13: 9780521591065

Acta Numerica surveys every year crucial advancements in numerical research. the themes and authors, selected via a exceptional overseas panel, offer a survey of articles notable of their caliber and breadth. This quantity comprises articles on multivariate integration; numerical research of semiconductor units; quickly transforms in utilized arithmetic; complexity matters in numerical research.

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Extra resources for Acta Numerica 1997: Volume 6

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0433 test is often distinctly more powerful than the WMW test. 0433 test. Thus, the BWS test has not only the advantage of being less conservative in comparison with the WMW test, but it is also more powerful for many distributions. And the difference in power is not (only) caused by the difference in size (Neuh¨auser, 2005a). The distribution of W is less discrete for large sample sizes; therefore the WMW test is less conservative. Because the difference in power between the tests BWS and WMW is not only due to the difference in size, the BWS test has a power benefit for larger sample sizes as well.

The rank sum test was introduced by Frank Wilcoxon in 1945; Henry Mann and Donald Whitney published their proposal in 1947. The test, however, is older. It was introduced at least six times in addition to Wilcoxon (1945) and Mann and Whitney (1947), see Kruskal (1957). The first who proposed the test was Gustav Deuchler in 1914, at that time at the University of T¨ ubingen, Germany. Deuchler (1914) suggested the following approach: Consider all n1 n2 pairs (Xi , Yj ). Each pair gets a score, this score being +1, −1, or 0, depending on whether the X value is larger, smaller, or equal to the Y -value of the pair.

050b Expon. 8. on the entire permutation null distribution (not simulated). b Based 42 Nonparametric Statistical Tests: A Computational Approach ˆ 1 and Q ˆ 2 , the best test is not always selected When using the selectors Q in practice. However, with the flexibility offered by the new approach with TAP T , the independence to the selector is no longer needed, and one can use the standardized test statistics Ti themselves as selectors. To be precise, one can perform a permutation test based on the following statistic: k TAP T 2 = i=1 I (Ti = max(T1 , .

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Acta Numerica 1997: Volume 6 by Arieh Iserles

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