A computationally efficient of robust mahalanobis distance based on MVV estimator

MCD is a well-known multivariate robust estimator. However, the computation of the estimator is not simple especially for large sample size due to the complexity of the objective function i.e. minimizing covariance determinant. Recently, an alternative objective function which is simpler and faster was introduced. The objective function is to minimize vector variance, which consequently will generate the estimator known as minimum vector variance (MVV). In this paper, a simulation study was conducted to compare the computational efficiency of the two estimators with regards to the number of operations in the computation of objective function and also iterations of the algorithm to convergence. The result showed that the computational efficiency of MVV is higher than MCD for small or large data set.