ORBi: Schyns Michael - RelaxMCD: smooth optimisation for the Minimum Covariance Determinant estimator

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


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/2268/12074

Title :	RelaxMCD: smooth optimisation for the Minimum Covariance Determinant estimator
Language :	English
Author, co-author :	Schyns, Michael [Université de Liège - ULg > HEC - Ecole de gestion de l'ULg > Informatique de gestion >]
	Haesbroeck, Gentiane [Université de Liège - ULg > Département de mathématique > Statistique (aspects théoriques) >]
	Critchley, Frank [The Open University > Department of Mathematics and Statistics > > >]
Publication date :	Apr-2010
Journal title :	Computational Statistics & Data Analysis
Publisher :	Elsevier Science
Volume :	54
Issue/season :	4
Pages :	843-857
Audience :	International
ISSN :	0167-9473
City :	Amsterdam
Country :	The Netherlands
Keywords :	[en] MCD estimator ; resampling algorithms ; k-means ; robustness
Abstract :	[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.
Research units :	QuantOM
Target :	Researchers
Permalink :	http://hdl.handle.net/2268/12074
Other URL :	http://dx.doi.org/10.1016/j.csda.2009.11.005
Mentions required by the publisher for OA :	The original publication is available at www.sciencedirect.com (csda)

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