DetMCD in a calibration framework

Abstract

The minimum covariance determinant (MCD) method is a robust estimator of multivariate location and scatter (Rousseeuw (1984)). Computing the exact MCD is very hard, so in practice one resorts to approximate algorithms. Most often the FASTMCD algorithm of Rousseeuw and Van Driessen (1999) is used. The FASTMCD algorithm is affine equivariant but not permutation invariant. Recently a deterministic algorithm, denoted as DetMCD, is developed which does not use random subsets and which is much faster (Hubert et al. (2010)). In this paper DetMCD is illustrated in a calibration framework. We focus on robust principal component regression and partial least squares regression, two very popular regression techniques for collinear data. We also apply DetMCD on data with missing elements after plugging it into the M-RPCR technique of Serneels and Verdonck (2009). © Springer-Verlag Berlin Heidelberg 2010.