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Robust statistic for the one-way MANOVA

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  • Todorov, Valentin
  • Filzmoser, Peter

Abstract

The Wilks' Lambda Statistic (likelihood ratio test, LRT) is a commonly used tool for inference about the mean vectors of several multivariate normal populations. However, it is well known that the Wilks' Lambda statistic which is based on the classical normal theory estimates of generalized dispersions, is extremely sensitive to the influence of outliers. A robust multivariate statistic for the one-way MANOVA based on the Minimum Covariance Determinant (MCD) estimator will be presented. The classical Wilks' Lambda statistic is modified into a robust one through substituting the classical estimates by the highly robust and efficient reweighted MCD estimates. Monte Carlo simulations are used to evaluate the performance of the test statistic under various distributions in terms of the simulated significance levels, its power functions and robustness. The power of the robust and classical statistics is compared using size-power curves, for the construction of which no knowledge about the distribution of the statistics is necessary. As a real data application the mean vectors of an ecogeochemical data set are examined.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 54 (2010)
Issue (Month): 1 (January)
Pages: 37-48

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Handle: RePEc:eee:csdana:v:54:y:2010:i:1:p:37-48

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  1. Gelper, Sarah & Croux, Christophe, 2007. "Multivariate out-of-sample tests for Granger causality," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3319-3329, April.
  2. Valentin Todorov, 2007. "Robust selection of variables in linear discriminant analysis," Statistical Methods and Applications, Springer, vol. 15(3), pages 395-407, February.
  3. Nath, Ravinder & Pavur, Robert, 1985. "A new statistic in the one-way multivariate analysis of variance," Computational Statistics & Data Analysis, Elsevier, vol. 2(4), pages 297-315, February.
  4. Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
  5. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
  6. Todorov, Valentin & Neykov, Neyko & Neytchev, Plamen, 1994. "Robust two-group discrimination by bounded influence regression. A Monte Carlo simulation," Computational Statistics & Data Analysis, Elsevier, vol. 17(3), pages 289-302, March.
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Cited by:
  1. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
  2. Valentin Todorov & Peter Filzmoser, . "An Object-Oriented Framework for Robust Multivariate Analysis," Journal of Statistical Software, American Statistical Association, vol. 32(i03).

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