Robust and Efficient One-Way MANOVA Tests

Aelst, Stefan Van; Willems, Gert

doi:10.1198/jasa.2011.tm09748

Cited by 30 publications

(12 citation statements)

References 30 publications

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“…Van Aelst and Willems [36] have derived robust one-way MANOVA tests without the assumption of multivariate normality, but requiring homogeneous covariance matrices. These are implemented in the R package FRB [37].…”

Section: Introductionmentioning

confidence: 99%

Parametric and nonparametric bootstrap methods for general MANOVA

Konietschke

Bathke

Harrar

et al. 2015

Journal of Multivariate Analysis

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a b s t r a c tWe develop parametric and nonparametric bootstrap methods for multi-factor multivariate data, without assuming normality, and allowing for covariance matrices that are heterogeneous between groups. The newly proposed, general procedure includes several situations as special cases, such as the multivariate Behrens-Fisher problem, the multivariate one-way layout, as well as crossed and hierarchically nested two-way layouts. We derive the asymptotic distribution of the bootstrap tests for general factorial designs and evaluate their performance in an extensive comparative simulation study. For moderate sample sizes, the bootstrap approach provides an improvement to existing methods in particular for situations with nonnormal data and heterogeneous covariance matrices in unbalanced designs. For balanced designs, less computationally intensive alternatives based on approximate sampling distributions of multivariate tests can be recommended.

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Section: Introductionmentioning

confidence: 99%

Parametric and nonparametric bootstrap methods for general MANOVA

Konietschke

Bathke

Harrar

et al. 2015

Journal of Multivariate Analysis

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“…From the point of view of estimation, the goal of this body of work has been the construction of estimators that can achieve both a high‐breakdown point and a high efficiency at the normal distribution (Maronna et al ., , Section 5.5). A non‐exhaustive list of supposedly robust and efficient techniques includes MM‐estimators (Maronna & Yohai, ; Van Aelst & Willems, ), tau‐estimators (Van Aelst et al ., ), the reweighted version of trimmed estimators (Cizek, ) and the forward search (Cerioli et al ., ; Johansen & Nielsen, ).…”

Section: Introductionmentioning

confidence: 99%

Reliable Robust Regression Diagnostics

Salini

Cerioli

Laurini

et al. 2015

Int Statistical Rev

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Motivated by the requirement of controlling the number of false discoveries that arises in several application fields, we study the behaviour of diagnostic procedures obtained from popular highbreakdown regression estimators when no outlier is present in the data. We find that the empirical error rates for many of the available techniques are surprisingly far from the prescribed nominal level. Therefore, we propose a simulation-based approach to correct the liberal diagnostics and reach reliable inferences. We provide evidence that our approach performs well in a wide range of settings of practical interest and for a variety of robust regression techniques, thus showing general appeal. We also evaluate the loss of power that can be expected from our corrections under different contamination schemes and show that this loss is often not dramatic. Finally, we detail some possible extensions that may further enhance the applicability of the method.

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“…We mention in passing that, with a burgeoning interesting in robust methods over the last few decades, there have been a variety of proposals for how to conduct robust tests of differences on mean vectors, mostly in the one-way MANOVA setting (e.g., Aelst & Willems, 2011;Todorov & Filzmoser, 2010). Generally speaking, these involve using more robust alternatives for mean vectors (medians, trimmed means, rank-based methods) and for covariance matrices (e.g., minimum covariance determinant (MCD) and minimum volume ellipsoid (MVE)).…”

Section: Homogeneity Of Variance In Manovamentioning

confidence: 99%

Visualizing Tests for Equality of Covariance Matrices

Friendly

Sigal

2018

The American Statistician

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This paper explores a variety of topics related to the question of testing the equality of covariance matrices in multivariate linear models, particularly in the MANOVA setting. The main focus is on graphical methods that can be used to address the evaluation of this assumption. We introduce some extensions of data ellipsoids, hypothesis-error (HE) plots and canonical discriminant plots and demonstrate how they can be applied to the testing of equality of covariance matrices. Further, a simple plot of the components of Box's M test is proposed that shows how groups differ in covariance and also suggests other visualizations and alternative test statistics. These methods are implemented and freely available in the heplots and candisc packages for R. Examples from the paper are available in supplementary materials.

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Robust and Efficient One-Way MANOVA Tests

Cited by 30 publications

References 30 publications

Parametric and nonparametric bootstrap methods for general MANOVA

Parametric and nonparametric bootstrap methods for general MANOVA

Reliable Robust Regression Diagnostics

Visualizing Tests for Equality of Covariance Matrices

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