On Fast Affine Equivariant Robust Scatter Estimation

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yunfei Wang*+ and Robert Serfling
• Companies: University of Texas at Dallas and University of Texas at Dallas
• Keywords: scatter estimation ; affine equivariance ; robustness ; Minimum Covariance Determinant ; spatial depth

Abstract

The Minimum Covariance Determinant (MCD) approach is a leading method for constructing multivariate location and scatter estimators that are affine equivariant and highly robust. Although direct computation of the MCD estimator is usually prohibitive, it can be computed approximately and more efficiently by the Fast-MCD algorithm. However, as shown in various experiments, even Fast-MCD becomes computationally prohibitive when the dimension of the data is sufficiently high. Here we introduce a new scatter estimator that is not only affine equivariant and robust, but also computationally more efficient. This estimator is based on the transformation-retransformation spatial outlyingness function and uses trimming to achieve robustness. Like the MCD, this estimator also becomes computationally burdensome for higher dimension, and so a fast version for it is developed. In a simulation study, the fast algorithm for the new scatter estimator is seen to be computationally efficient and much faster than Fast-MCD for high dimensions (for example, greater than 500). Other properties of the new scatter estimator will also be discussed.