Reference : An Easy Way to Increase the Finite-Sample Efficiency of the Resampled Minimum Volume ...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/39892
An Easy Way to Increase the Finite-Sample Efficiency of the Resampled Minimum Volume Ellipsoid Estimator
English
Croux, Christophe [Katholieke Universiteit Leuven - KUL > > > >]
Haesbroeck, Gentiane mailto [Université de Liège - ULg > Département de mathématique > Statistique mathématique >]
1997
Computational Statistics & Data Analysis
Elsevier Science
25
125-141
Yes (verified by ORBi)
International
0167-9473
Amsterdam
The Netherlands
[en] Breakdown point ; Finite-sample efficiency ; Location estimation ; Minimum volume ellipsoid ; Robustness
[en] In a robust analysis, the minimum volume ellipsoid (MVE) estimator is very often used to estimate both multivariate location and scatter. The MVE estimator for the scatter matrix is defined as the smallest ellipsoid covering half of the observations, while the MVE location estimator is the midpoint of that ellipsoid. The MVE estimators can be computed by minimizing a certain criterion over a high-dimensional space. In practice, one mostly uses algorithms based on minimization of the objective function over a sequence of trial estimates. One of these estimators uses a resampling scheme, and yields the (p + 1)-subset estimator. In this note, we show how this estimator can easily be adapted, yielding a considerable increase of statistical efficiency at finite samples. This gain in precision is also observed when sampling from contaminated distributions, and it becomes larger when the dimension increases. Therefore, we do not need more computation time nor do we lose robustness properties. Moreover, only a few lines have to be added to existing computer programs. The key idea is to average over several trials close to the optimum, instead of just picking out the trial with the lowest value for the objective function. The resulting estimator keeps the equivariance and robustness properties of the original MVE estimator. This idea can also be applied to several other robust estimators, including least-trimmed-squares regression.
Researchers
http://hdl.handle.net/2268/39892
also: http://hdl.handle.net/2268/39896
10.1016/S0167-9473(96)00088-6

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