A fast algorithm for the minimum covariance determinant estimator

Published on Aug 1, 1999in Technometrics2.09
· DOI :10.2307/1270566
Peter J. Rousseeuw52
Estimated H-index: 52
Katrien Van Driessen5
Estimated H-index: 5
The minimum covariance determinant (MCD) method of Rousseeuw is a highly robust estimator of multivariate location and scatter. Its objective is to find h observations (out of n) whose covariance matrix has the lowest determinant. Until now, applications of the MCD were hampered by the computation time of existing algorithms, which were limited to a few hundred objects in a few dimensions. We discuss two important applications of larger size, one about a production process at Philips with n = 677 objects and p = 9 variables, and a dataset from astronomy with n = 137,256 objects and p = 27 variables. To deal with such problems we have developed a new algorithm for the MCD, called FAST-MCD. The basic ideas are an inequality involving order statistics and determinants, and techniques which we call “selective iteration” and “nested extensions.” For small datasets, FAST-MCD typically finds the exact MCD, whereas for larger datasets it gives more accurate results than existing algorithms and is faster by orders...
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