Abstract
Hypothesis tests and confidence intervals based on the classical Hotelling T 2 statistic can be adversely affected by outliers. Therefore, we construct an alternative inference technique based on a statistic which uses the highly robust MCD estimator of Rousseeuw (1984) instead of the classical mean and covariance matrix. The distribution of this new statistic differs from the classical one. Similarly to the classical T 2 distribution, we obtain a multiple of a certain F-distribution. It is shown through a Monte Carlo study that this approximation is very accurate, both at the normal model and at contamination models.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Croux, C. and Haesbroeck, G. (1999). Influence and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator. Journal of Multivariate Analysis, 71, 161–190.
Hardin, J. and Rocke, D.M. (2001). The Distribution of Robust Distances. Technical Report, Univ. of California at Davis.
Johnson, R.A. and Wichern, D.W. (1988). Applied Multivariate Statistical Analysis. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
Lopuhaä, H.P. (1999). Asymptotics of Reweighted Estimators of Multivariate Location and Scatter. The Annals of Statistics, 27, 1638–1665.
Lopuhaä, H.P. and Rousseeuw, P.J. (1991). Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices. The Annals of Statistics, 19 229–248.
Mardia, K.V., Kent J.T. and Bibby J.M. (1995). Multivariate Analysis. Academic Press Ltd., London.
Pison, G., Van Aelst, S. and Willems, G. (2002). Small Sample Corrections for LTS and MCD. Metrika, to appear.
Rousseeuw, P.J. (1984). Least Median of Squares Regression. Journal of the American Statistical Association, 79, 871–880.
Rousseeuw, P.J. and Van Driessen, K. (1999). A Fast Algorithm for the Minimum Covariance Determinant Estimator. Technometrics, 41, 212–223.
Rousseeuw, P.J. and Van Zomeren, B.C. (1990). Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association, 85, 633–651.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Willems, G., Pison, G., Rousseeuw, P.J., Van Aelst, S. (2002). A Hotelling Test Based on MCD. In: Härdle, W., Rönz, B. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57489-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-57489-4_12
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1517-7
Online ISBN: 978-3-642-57489-4
eBook Packages: Springer Book Archive