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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
Abstract
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...
  • References (27)
  • Citations (1250)
References27
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#1David M. Rocke (UC Davis: University of California, Davis)H-Index: 47
#2David L. Woodruff (UC Davis: University of California, Davis)H-Index: 31
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#2Shen Wang (HIT: Harbin Institute of Technology)
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#1L.A. Bull (University of Sheffield)H-Index: 1
#2T.J. Rogers (University of Sheffield)H-Index: 2
Last.Nikolaos Dervilis (University of Sheffield)H-Index: 8
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#1Jinting Guan (Ha Tai: Xiamen University)H-Index: 2
#2Jinting Guan (Ha Tai: Xiamen University)H-Index: 2
Last.Pak Sham (HKU: University of Hong Kong)H-Index: 106
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#1Saeid Ghasemzadeh (AUT: Amirkabir University of Technology)H-Index: 1
#2Abbas Maghsoudi (AUT: Amirkabir University of Technology)H-Index: 9
Last.Mark J. Mihalasky (USGS: United States Geological Survey)H-Index: 3
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View next paperRobust $M$-Estimators of Multivariate Location and Scatter