Reference : RelaxMCD: smooth optimisation for the Minimum Covariance Determinant estimator |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/2268/12074 | |||

RelaxMCD: smooth optimisation for the Minimum Covariance Determinant estimator | |

English | |

Schyns, Michael [Université de Liège - ULiège > HEC - École de gestion de l'ULiège > Informatique de gestion >] | |

Haesbroeck, Gentiane [Université de Liège - ULiège > Département de mathématique > Statistique (aspects théoriques) >] | |

Critchley, Frank [The Open University > Department of Mathematics and Statistics > > >] | |

Apr-2010 | |

Computational Statistics and Data Analysis | |

Elsevier Science | |

54 | |

4 | |

843-857 | |

Yes (verified by ORBi) | |

International | |

0167-9473 | |

Amsterdam | |

The Netherlands | |

[en] MCD estimator ; resampling algorithms ; k-means ; robustness | |

[en] The Minimum Covariance Determinant (MCD) estimator is a highly robust procedure for estimating the
center and shape of a high dimensional data set. It consists of determining a subsample of h points out of n which minimizes the generalized variance. By definition, the computation of this estimator gives rise to a combinatorial optimization problem, for which several approximative algorithms have been developed. Some of these approximations are quite powerful, but they do not take advantage of any smoothness in the objective function. In this paper, focus is on the approach outlined in a general framework in Critchley et al. (2009) and which transforms any discrete and high dimensional combinatorial problem of this type into a continuous and low-dimensional one. The idea is to build on the general algorithm proposed by Critchley et al. (2009) in order to take into account the particular features of the MCD methodology. More specifically, both the adaptation of the algorithm to the specific MCD target function as well as the comparison of this “specialized” algorithm with the usual competitors for computing MCD are the main goals of this paper. The adaptation focuses on the design of “clever” starting points in order to systematically investigate the search domain. Accordingly, a new and surprisingly efficient procedure based on the well known k-means algorithm is constructed. The adapted algorithm, called RelaxMCD, is then compared by means of simulations and examples with FASTMCD and the Feasible Subset Algorithm, both benchmark algorithms for computing MCD. As a by-product, it is shown that RelaxMCD is a general technique encompassing the two others, yielding insight about their overall good performance. | |

QuantOM | |

Researchers | |

http://hdl.handle.net/2268/12074 | |

10.1016/j.csda.2009.11.005 | |

http://dx.doi.org/10.1016/j.csda.2009.11.005 | |

The original publication is available at www.sciencedirect.com (csda) |

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