Robust statistic for the one-way MANOVA

Todorov, Valentin; Filzmoser, Peter

doi:10.1016/j.csda.2009.08.015

Cited by 73 publications

(45 citation statements)

References 17 publications

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“…The next large group of classes are the methods for robust principal component analysis (PCA) including ROBPCA of Hubert et al (2005), spherical principal components (SPC) of Locantore et al (1999), the projection pursuit algorithms of Croux and Ruiz-Gazen (2005) and Croux et al (2007). Further applications implemented in the framework are linear and quadratic discriminant analysis (see Todorov and Pires 2007, for a review), multivariate tests Todorov and Filzmoser 2010) and outlier detection tools.…”

Section: Introductionmentioning

confidence: 99%

An Object-Oriented Framework for Robust Multivariate Analysis

Todorov¹,

Filzmoser²

2009

J. Stat. Soft.

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283

197

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Taking advantage of the S4 class system of the programming environment R, which facilitates the creation and maintenance of reusable and modular components, an objectoriented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for principal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov.

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Section: Introductionmentioning

confidence: 99%

An Object-Oriented Framework for Robust Multivariate Analysis

Todorov¹,

Filzmoser²

2009

J. Stat. Soft.

Self Cite

283

197

View full text Add to dashboard Cite

show abstract

“…It also has good asymptotic properties that compare favourably with those of other high-breakdown estimators (Butler et al 1993;Croux and Haesbroeck 1999). For these reasons the MCD estimator has gained much popularity, not only for outlier identification but also as an ingredient of many robust multivariate techniques (Croux and Haesbroeck 2000;Willems et al 2002;Pison and Van Aelst 2004;Rousseeuw et al 2004;Todorov 2006;Todorov and Filzmoser 2008).…”

mentioning

confidence: 99%

Controlling the size of multivariate outlier tests with the MCD estimator of scatter

2008

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Multivariate outlier detection requires computation of robust distances to be compared with appropriate cut-off points. In this paper we propose a new calibration method for obtaining reliable cut-off points of distances derived from the MCD estimator of scatter. These cut-off points are based on a more accurate estimate of the extreme tail of the distribution of robust distances. We show that our procedure gives reliable tests of outlyingness in almost all situations of practical interest, provided that the sample size is not much smaller than 50. Therefore, it is a considerable improvement over all the available MCD procedures, which are unable to provide good control over the size of multiple outlier tests for the data structures considered in this paper.

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“…Hence, inference based on such statistics can be severely distorted when the data is contaminated by outliers (see e.g. Todorov and Filzmoser 2010). A common approach to robustify statistical inference procedures is to replace the classical nonrobust estimates in these procedures by robust estimates (see e.g.…”

Section: Johnson and Wichern 2002)mentioning

confidence: 99%

“…It simply replaces each observation with its rank (componentwise) over all groups and then applies Wilks' Lambda. The second test (Todorov and Filzmoser, 2010) uses a test statistic based on weighted MCD estimators and obtains the null distribution by Monte Carlo simulation from a multivariate normal distribution, as implemented in the R-package rrcov (Todorov and Filzmoser 2009). For both the classical test and its rank-transformed version, the approximation…”

Section: Finite-sample Robustness Of the Levelmentioning

confidence: 99%

Robust and Efficient One-Way MANOVA Tests

Aelst

Willems

2011

Journal of the American Statistical Association

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We propose robust tests as alternatives to the classical Wilks' Lambda test in one-way MANOVA. The robust tests use highly robust and efficient multi-sample multivariate S-or MM-estimators instead of the empirical covariances. The properties of several robust test statistics are compared. Under the null hypothesis, the distribution of the test statistics is proportional to a chi-square distribution. As an alternative to the asymptotic distribution, we develop a fast robust bootstrap method to estimate the distribution under the null hypothesis. We show when it is asymptotically correct to estimate the null distribution in this way and we use simulations to verify the performance of the bootstrap based tests in finite samples. We also investigate the power of the new tests, as well as their robustness against outliers. Finally, we illustrate the use of these robust test statistics on a real data example. Some additional results are provided as supplemental material.

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Robust statistic for the one-way MANOVA

Cited by 73 publications

References 17 publications

An Object-Oriented Framework for Robust Multivariate Analysis

An Object-Oriented Framework for Robust Multivariate Analysis

Controlling the size of multivariate outlier tests with the MCD estimator of scatter

Robust and Efficient One-Way MANOVA Tests

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