The Nonparametric Behrens‐Fisher Problem: Asymptotic Theory and a Small‐Sample Approximation

By Edgar Brunner, U. Munzel. 2000

614 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a51145f1c58f3645e1a333f4602125498b2f09d8

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In Statistics and Probability

Citations in the corpus

The Wilcoxon–Mann–Whitney Procedure Fails as a Test of Medians (2018, background): “Brunner and Munzel (2000), present a derivation of a WMW test variation addressing the Behrens-Fisher problem, that explicitly allows for the presence of ties.”
A studentized permutation test for the nonparametric Behrens-Fisher problem in paired data (2012, methodology): “Therefore, testing the null hypothesis H0 : p = 1/2 is known as the nonparametric Behrens-Fisher problem (Brunner and Munzel, 2000). Munzel (1999b) proposed a test procedure for H0 : p = 1/2 and a small sample approximation in matched pairs. His test is widely used by practitioners (Krone et al., 20”
A Bootstrap Test of Stochastic Equality of Two Populations (2005, methodology): “KEY WORDS: Brunner-Munzel test; Mann-WhitneyU -test; Rank Welch test; Stochastic equality; Wilcoxon rank sum test.”
Permutation inference for the general linear model (2014, methodology): “Statistics that can be used include, for instance, those based on ranks of observations (Brunner and Munzel, 2000; Rorden et al., 2007), derived from regression methods other than least squares (Cade and Richards, 1996) or that are robust to outliers (Sen, 1968; Theil, 1950).”
Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules (2010, methodology): “Brunner and Munzel (2000) showed that comparing TNBF = φ(F̂ , Ĝ)− 12√ VJ to a t-distribution with degrees of freedom estimated using a method similar to Satterthwaite’s gives a PAV test under Perspective 10.”
Rank-based multiple test procedures and simultaneous confidence intervals (2012, background): “For a detailed discussion of the hypotheses formulated above we refer to Akritas et al. (1997) [1] and Brunner and Munzel (2000) [8].”
nparcomp: An R Software Package for Nonparametric Multiple Comparisons and Simultaneous Confidence Intervals (2015, methodology): “For a detailed discussion of the hypotheses formulated above we refer to Akritas, Arnold, and Brunner (1997) and Brunner and Munzel (2000).”
Rank‐based procedures in factorial designs: hypotheses about non‐parametric treatment effects (2016, methodology): “…of tN =√N.p̂−p/ under the following framework: min 1 i d .ni/→∞ such that N=ni N0 <∞ for all i=1, : : : , d: .8/ We first summarize some well-known results about the asymptotic distribution of √ N.ŵli − wli/=√N. ∫ F̂ ldF̂ i − ∫ FldFi/, where N =Σdi=1ni; see, for example, Brunner and Munzel (2000).”
Improving Lesion-Symptom Mapping (2007, background): “Brunner and Munzel (2000) have recently described a rank order test that is essentially assumption free.”
Measures of sociality: two different views of group size (2008, positive): “Here, the Brunnere Munzel test (Brunner & Munzel 2000), or the bootstrap rank Welch test (Reiczigel et al. 2005b) is proposed.”