The Efficiency of Some Nonparametric Competitors of the t-Test

By J. Hodges, Erich Leo Lehmann. 1956

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “The proposed method corresponds to maximizing the Hodges and Lehmann asymptotic relative efficiency (Hodges and Lehmann 1956).”
Optimal procedures based on interdirections and pseudo-Mahalanobis ranks for testing multivariate elliptic white noise against ARMA dependence (2002, methodology): “Note that the sequence of lower bounds ( 14 ) is monotonically decreasing for k 2; as the dimension k tends to innit y, it tends to 9=16 = 0:5625.”
Kendall's tau for serial dependence (2000, background): “thereby providing a serial analogue to the celebrated 0.864 lower bound given by Hodges & Lehmann (1956) for the asymptotic relative efficiency of Wilcoxon’s statistic with respect to Student’s test statistic.”
Parametric versus nonparametrics: two alternative methodologies (2009, background): “On the other hand, it was shown by Hodges and Lehmann 11 that for all F”
Applied Multivariate Statistical Analysis (2003, background): “Hodges and Lehman (1956) showed that, given a mean of zero and unit variance, the (compact support) density which minimizes ∫ f 2 is uniquely given by f(z) = max{0, c(b(2) − z(2))}, where c = 3/(20 √ 5) and b = √ 5.”
Optimal tests for multivariate location based on interdirections and pseudo-Mahalanobis ranks (2002, methodology): “…argument used in Chernoff and Savage (1958); see Appendix C. Proposition 5 also allows for extension of the famous Hodges–Lehmann “.864 result” [Hodges and Lehmann (1956)] by computing, for any dimension k, the lower bound for the asymptotic relative efficiency of the Wilcoxon procedure…”
Optimal asymmetric kernels (2004, background): “If there are no a priori grounds for believing that the underlying density f(x) is skewed, then the derivations in Hodges and Lehmann (1956) or Epanechnikov (1969) apply.”
Nonparametric Statistical Inference (2020, methodology): “The Terry (1952) and Hoeffding (1951) or the Fisher-Yates normal scores test uses the weights ai 1⁄4 EðxðiÞÞ, where xðiÞ is the ith-order LINEAR RANK TESTS FOR THE LOCATION PROBLEM 307”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, background): “Their work provides the first multivariate, exactly distribution-free analogs of the classical results in Hodges and Lehmann (1956) and Chernoff and Savage (1958).”