Title: Efficient computation of the minimum weighted covariance determinant estimator
Authors: Jurjen Duintjer Tebbens - Institute of Computer Science of the Czech Academy of Sciences (Czech Republic)
Jan Kalina - The Czech Academy of Sciences, Institute of Information Theory and Automation (Czech Republic) [presenting]
Abstract: We study efficient algorithms for robust estimators of multivariate location and scatter. First, we propose an efficient algorithm for the existing Minimum Weighted Covariance Determinant (MWCD) estimator, which can be interpreted as a weighted analogy of the popular Mininum Covariance Determinant (MCD) estimator. The algorithm exploits suitable tools of numerical linear algebra. Further, we propose a new version of the estimator, which is again based on implicit weights assigned to individual observations, but an original idea allows the estimator to be computationally much more efficient. Our theoretical results include the asymptotic efficiency and breakdown point derived for the novel method. Nevertheless, the main contribution is again a proposal of an efficient algorithm for its computation.