Robust statistic for the one-way MANOVA
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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- Russell Davidson & James G. MacKinnon, 1994.
"Graphical Methods for Investigating the Size and Power of Hypothesis Tests,"
903, Queen's University, Department of Economics.
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- 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.
- 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.
- Siani, Carole & de Peretti, Christian, 2007. "Analysing the performance of bootstrap neural tests for conditional heteroskedasticity in ARCH-M models," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2442-2460, February.
- Hubert, Mia & Van Driessen, Katrien, 2004. "Fast and robust discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 301-320, March.
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