Title 



Location adjustment for the minimum volume ellipsoid estimator
 
Author 



 
Abstract 



Estimating multivariate location and scatter with both affine equivariance and positive breakdown has always been difficult. A wellknown estimator which satisfies both properties is the Minimum Volume Ellipsoid Estimator (MVE). Computing the exact MVE is often not feasible, so one usually resorts to an approximate algorithm. In the regression setup, algorithms for positivebreakdown estimators like Least Median of Squares typically recompute the intercept at each step, to improve the result. This approach is called intercept adjustment. In this paper we show that a similar technique, called location adjustment, can be applied to the MVE. For this purpose we use the Minimum Volume Ball (MVB), in order to lower the MVE objective function. An exact algorithm for calculating the MVB is presented. As an alternative to MVB location adjustment we propose L1 location adjustment, which does not necessarily lower the MVE objective function but yields more efficient estimates for the location part. Simulations compare the two types of location adjustment. We also obtain the maxbias curves of both L1 and the MVB in the multivariate setting, revealing the superiority of L1.   
Language 



English
 
Source (journal) 



Statistics and computing.  London  
Publication 



London : 2002
 
ISSN 



09603174
 
Volume/pages 



12:3(2002), p. 191200
 
ISI 



000178716400001
 
Full text (Publishers DOI) 


  
Full text (publishers version  intranet only) 


  
