Metode Minimum Volume Ellipsoid (MVE) dan Minimum Covariance Determinant (MCD) dalam Mengestimasi Matriks Kovarian pada Data Multivariat

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. This study aims to estimate the covariance matrix that is not affected by outliers in multivariate data using the MVE and MCD methods. In the MVE method, estimation is done by finding the smallest ellipsoid that contains most of the data points, which then becomes a representation of the dataset. Meanwhile, in the MCD method does not use an ellipsoid that contains h point, but only uses h points to estimate the covariance matrix. 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. For these results, it can be seen that both the MVE and MCD methods are suitable for estimating the covariance matric in multivariate data.