Approximations to Some Test Statistics for Permutation Tests in a Completely Randomized Design1

Robinson, John

doi:10.1111/j.1467-842x.1983.tb00389.x

Cited by 14 publications

(1 citation statement)

References 8 publications

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“….. These conditions extend slightly those of Robinson (1983), and, as shown there, they imply that, as N → ∞, either |λ + N | → 0 or sup j N −1/2 |q + N j | → 0, for = 1, 2, . .…”

Section: Proof Of Asymptotic Distribution Of Test Statisticssupporting

confidence: 80%

Generalized discriminant analysis based on distances

Anderson

Robinson

2003

Aus NZ J of Statistics

648

369

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This paper describes a method of generalized discriminant analysis based on a dissimilarity matrix to test for differences in a priori groups of multivariate observations. Use of classical multidimensional scaling produces a low-dimensional representation of the data for which Euclidean distances approximate the original dissimilarities. The resulting scores are then analysed using discriminant analysis, giving tests based on the canonical correlations. The asymptotic distributions of these statistics under permutations of the observations are shown to be invariant to changes in the distributions of the original variables, unlike the distributions of the multi-response permutation test statistics which have been considered by other workers for testing differences among groups. This canonical method is applied to multivariate fish assemblage data, with Monte Carlo simulations to make power comparisons and to compare theoretical results and empirical distributions. The paper proposes classification based on distances. Error rates are estimated using cross-validation.

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Section: Proof Of Asymptotic Distribution Of Test Statisticssupporting

confidence: 80%