Minimum Vollume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) Methods for Estimating Covariance Matrix in Multivariate Data

Ananda Ifrajiani Khair; Sutarman Sutarman

doi:10.30829/zero.v8i1.20808

Minimum Vollume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) Methods for Estimating Covariance Matrix in Multivariate Data

Ananda Ifrajiani Khair, Sutarman Sutarman

Abstract

Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) are robust methods used to handle the outlier problem. Outliers are points that appear to deviate significantly from other data sample points that can have a significant effect on the results of the analysis, so a robust method is needed to solve this problem. MVE and MCD have a high breakdown point or level of resistance to outliers, which is 50%, so that it can overcome the influence of extreme outliers. Based on this research, it is known that by using the same data, the MVE and MCD methods produce more robust estimates that were not affected by outliers. The non robust method just found 10 outliers, while the MVE method found that were 276 data points detected as outliers and for the MCD method, the estimation result is with 257 data points detected as outliers.

Keywords

Covariance Matrix; MCD Method; Multivariate Data; MVE Method; Outlier

Full Text:

PDF

References

G. M. Oyeyemi and R. A. Ipinyomi, “A robust method of estimating covariance matrix in multivariate data analysis,” Analele Ştiinţifice ale Univ. »Alexandru Ioan Cuza« din Iaşi. Ştiinţe Econ., vol. 56, no. 1, pp. 586–601, 2009.

F. E. Grubbs, “Procedures for Detecting Outlying Observations in Samples,” Technometrics, vol. 11, no. 1, pp. 1–21, 1969, doi: 10.1080/00401706.1969.10490657.

T. Zaman and H. Bulut, “Modified regression estimators using robust regression methods and covariance matrices in stratified random sampling,” Commun. Stat. - Theory Methods, vol. 49, no. 14, pp. 3407–3420, 2020, doi: 10.1080/03610926.2019.1588324.

P. Pfeiffer and P. Filzmoser, “Robust statistical methods for high-dimensional data, with applications in tribology,” Anal. Chim. Acta, vol. 1279, no. August, p. 341762, 2023, doi: 10.1016/j.aca.2023.341762.

Rousseeuw, P. J, and K. van Driessen, “A Fast Algorithm for the Minimum Covariance Determinant Estimator,” Technometrics, vol. 41, no. 3, pp. 212–223, 1999.

F. P. Hidayatulloh, D. Yuniarti, and S. Wahyuningsih, “Regresi Robust Dengan Metode Estimasi-S,” Eksponensial, vol. 6, no. 2, pp. 163–170, 2015.

S. F. Møller, J. Von Frese, and R. Bro, “Robust methods for multivariate data analysis,” J. Chemom., vol. 19, no. 10, pp. 549–563, 2005, doi: 10.1002/cem.962.

A. S. Hadi, “Identifying Multiple Outliers in Multivariate Data,” J. R. Stat. Soc., vol. 54, no. 3, pp. 761–771, 1992.

S. Van Aelst and P. Rousseeuw, “Minimum volume ellipsoid,” Wiley Interdiscip. Rev. Comput. Stat., vol. 1, no. 1, pp. 71–82, 2009, doi: 10.1002/wics.19.

A. S. Hadi, A. H. M. Rahmatullah Imon, and M. Werner, “Detection of outliers,” Wiley Interdiscip. Rev. Comput. Stat., vol. 1, no. 1, pp. 57–70, 2009, doi: 10.1002/wics.6.

V. Barnett and T. Lewis, “Outliers in statistical data, second edition,” John Wiley Sons, p. 463, 1994.

V. Chandola, A. Banerjee, and V. Kumar, “Anomaly Detection : A Survey,” vol. 41, no. 3, pp. 1–58, 2009, doi: 10.1145/1541880.1541882.

K. Singh and M. Cantt, “Outlier Detection : Applications And Techniques,” vol. 9, no. 1, pp. 307–323, 2012.

A. Boukerche, L. Zheng, and O. Alfandi, “Outlier Detection: Methods, Models, and Classification,” ACM Comput. Surv., vol. 53, no. 3, 2020, doi: 10.1145/3381028.

G. Strang, Introduction to Linear Algebra, Fourth Edition, 4th Editio. Wellesley - Cambridge Press, 2009.

DOI: http://dx.doi.org/10.30829/zero.v8i1.20808

Refbacks

There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Department of Mathematics
Faculty of Science and Technology
Universitas Islam Negeri Sumatera Utara Medan

Email: mtk.saintek@uinsu.ac.id

Username
Password
Remember me