A novel definition of the multivariate coefficient of variation

[en] The coefficient of variation CV (%) is widely used to measure the relative variation of a random variable to its mean or to assess and compare the performance of analytical techniques/equipments. A review is made of the existing multivariate extensions of the univariate CV where, instead of a random variable, a random vector is considered, and a novel definition is proposed. The multivariate CV obtained only requires the calculation of the mean vector, the covariance matrix and simple quadratic forms. No matrix inversion is needed which makes the new approach equally attractive inhigh dimensional as in very small sample size problems. As an illustration, the method is applied to electrophoresis data from external quality assessment in laboratory medicine, to phenotypic characteristics of pocket gophers and to a microarray data set.

Disciplines :

Public health, health care sciences & services

Author, co-author :

Albert, Adelin ; Université de Liège - ULiège > Département des sciences de la santé publique > Informatique médicale et biostatistique - Département de mathématique

Zhang, Lixin ; Université de Liège - ULiège > Département des sciences de la santé publique > Informatique médicale et biostatistique

Language :

English

Title :

A novel definition of the multivariate coefficient of variation

Publication date :

2010

Journal title :

Biometrical Journal

ISSN :

0323-3847

eISSN :

1521-4036

Publisher :

Wiley, Chichester, United Kingdom

Volume :

Issue :

Pages :

667-675

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 27 March 2012

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Bibliography

Aitchison, J. ( 1986). The Statistical Analysis of Compositional Data. Monographs on Statistics and Applied Probability. Chapman & Hall, London.
Barr, D. R. and Sherrill, E. T. ( 1999). Mean and variance of truncated normal distributions. The American Statistician 53, 357-361.
Bennett, B. M. ( 1977). On multivariate coefficients of variation. Statistical Papers 18, 123-128.
Budsaba, K. and Smith, C. E. ( 2006). Detecting a random component in a two compartment model: an independent random effects simulation study. Thammasat International Journal Science Technology 11, 1-13.
Cramér, H. ( 1974). Mathematical Methods of Statistics. Princeton University Press, Princeton.
Efron, B. ( 2009). Empirical Bayes estimates for large-scale prediction problems. Journal of the American Statistical Association 104, 1015-1028.
Efron, B. and Tibshirani, R. J. ( 1993). An Introduction to the Bootstrap. Chapman & Hall, New York.
Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueraz, G. and Barceló-Vidal, C. ( 2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology 35, 279-300.
Golub, T. R., Slonim, D. K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J. P., Coller, H., Loh, M. L., Downing, J. R., Caligiuri, M. A., Bloomfield, C. D. and Lander, E. S. ( 1999). Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286, 531-537.
Harville, D. A. ( 2008). Matrix Algebra from a Statistician's Perspective (2nd edn.) Springer, New York.
R Development Core Team. ( 2009). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN: 3-900051-07-0.
Reyment, R. A. ( 1960). Studies on Nigerian Upper Cretaceous and Lower Tertiary Ostracoda: part 1. Senonian and Maastrichtian Ostracoda. Stockholm Contributions in Geology 7, 1-238.
Rousseeuw, P. J. and Van Driessen, K. ( 1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212-223.
Soulé, M. E. and Zegers, G. P. ( 1996). Phenetics of natural populations. V. genetic correlates of phenotypic variation in the pocket gopher (Thomomys bottae) in California. Journal of Heredity 87, 341-350.
Underhill, L. G. ( 1990). The coefficient of variation biplot. Journal of Classification 7, 241-256.
Van Valen, L. ( 1974). Multivariate structural statistics in natural history. Journal of Theoretical Biology 45, 235-247.
Van Valen, L. ( 2005). The statistics of variation. In: Hallgrímsson, B. and Hall, B. K. (Eds.). Variation: a Central Concept in Biology, Elsevier, Burlington, 29-47.
Voinov, V. G. and Nikulin, M. S. ( 1996). Unbiased Estimators and Their Applications, Vol. 2, Multivariate Case. Kluwer, Dordrecht.
Zhang, L., Albarède, S., Dumont, G., Van Campenhout, C., Libeer, J. C. and Albert, A. ( 2010). The multivariate coefficient of variation for comparing serum protein electrophoresis techniques in External Quality Assessment schemes. Accreditation and Quality Assurance 15, 351-357.
Zhang, L., Van Campenhout, C., Devleeschouwer, N., Libeer, J. C. and Albert, A. ( 2008). Statistical analysis of serum protein electrophoresis results in External Quality Assessment schemes. Accreditation and Quality Assurance 13, 149-155.