Alternative Estimator for Multivariate Location and Scatter Matrix in the Presence of Outlier

摘要

It is generally known that in estimating location and scatter matrix of multivariate data when outliers are presents, the method of classical is not robust. The Maximum Likelihood Estimator (MLE) is always very sensitive to some deviations from the assumptions made on the data, especially, presence of outliers. To get over the above stated problem, many alternative estimators that are robust have been proposed in the last decades. Some of these estimators include the Minimum Covariance Determinant (MCD), the Minimum Volume Ellipsoid (MVE), S-Estimators, M-Estimators and Minimum Regularized Covariance Determinant (MRCD) among others. All the methods converged on tackling the problem of robust estimation by finding a sufficiently large subset of the data. In this paper, a robust method of estimating multivariate location and scatter matrix in the presence of outliers is proposed. The proposed estimator is obtained using the best units (samples) from the available data set that satisfied a set of three optimality criteria (CA,CH,CG).The performance of the proposed robust method was compared with two of the existing robust methods (MCD and MVE) and the classical method with their application in Principal component analysis data simulation. The measure of performance used was the Mean Square Errors (MSE) of the characteristic roots (eigen-values) of the variance-covariance matrix. Generally, the proposed alternative method is better than other robust methods and classical method, when the level of magnitude of outliers is small and also performed considerably well with MCD and MVE when the level of magnitude is high at all percentages of outliers.