References of "Haesbroeck, Gentiane"
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See detailImplementing the Bianco and Yohai estimator for logistic regression
Croux, C.; Haesbroeck, Gentiane ULg

in Computational Statistics & Data Analysis (2003), 44(1-2), 273-295

A fast and stable algorithm to compute a highly robust estimator for the logistic regression model is proposed. A criterium. for the existence of this estimator at finite samples is derived and the ... [more ▼]

A fast and stable algorithm to compute a highly robust estimator for the logistic regression model is proposed. A criterium. for the existence of this estimator at finite samples is derived and the problem of the selection of an appropriate loss function is discussed. It is shown that the loss function can be chosen such that the robust estimator exists if and only if the maximum likelihood estimator exists. The advantages of using a weighted version of this estimator are also considered. Simulations and an example give further support for the good performance of the implemented estimators. (C) 2003 Elsevier B.V. All rights reserved. [less ▲]

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See detailThe breakdown behavior of the maximum likelihood estimator in the logistic regression model
Croux, C.; Flandre, C.; Haesbroeck, Gentiane ULg

in Statistics & Probability Letters (2002), 60(4), 377-386

In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in the logistic regression model. We formally prove that the ML-estimator never explodes to infinity, but rather ... [more ▼]

In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in the logistic regression model. We formally prove that the ML-estimator never explodes to infinity, but rather breaks down to zero when adding severe outliers to a data set. An example confirms this behavior. (C) 2002 Published by Elsevier Science B.V. [less ▲]

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See detailLocation adjustment for the minimum volume ellipsoid estimator
Croux, C.; Haesbroeck, Gentiane ULg; Rousseeuw, P. J.

in Statistics and Computing (2002), 12(3), 191-200

Estimating multivariate location and scatter with both affine equivariance and positive breakdown has always been difficult. A well-known estimator which satisfies both properties is the Minimum Volume ... [more ▼]

Estimating multivariate location and scatter with both affine equivariance and positive breakdown has always been difficult. A well-known 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 positive-breakdown 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 L-1 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 L-1 and the MVB in the multivariate setting, revealing the superiority of L-1. [less ▲]

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See detailMaxbias curves of robust location estimators based on subranges
Croux, C.; Haesbroeck, Gentiane ULg

in Journal of Nonparametric Statistics (2002), 14(3), 295-306

A maxbias curve is a powerful tool to describe the robustness of an estimator. It tells us how much an estimator can change due to a given fraction of contamination. In this paper, maxbias curves are ... [more ▼]

A maxbias curve is a powerful tool to describe the robustness of an estimator. It tells us how much an estimator can change due to a given fraction of contamination. In this paper, maxbias curves are computed for some univariate location estimators based on subranges: midranges, trimmed means and the univariate Minimum Volume Ellipsoid (MVE) location estimators. These estimators are intuitively appealing and easy to calculate. [less ▲]

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See detailA note on finite-sample efficiencies of estimators for the minimum volume ellipsoid
Croux, C.; Haesbroeck, Gentiane ULg

in Journal of Statistical Computation & Simulation (2002), 72(7), 585-596

Among the most well known estimators of multivariate location and scatter is the Minimum Volume Ellipsoid (MVE). Many algorithms have been proposed to compute it. Most of these attempt merely to ... [more ▼]

Among the most well known estimators of multivariate location and scatter is the Minimum Volume Ellipsoid (MVE). Many algorithms have been proposed to compute it. Most of these attempt merely to approximate as close as possible the exact MVE, but some of them led to the definition of new estimators which maintain the properties of robustness and affine equivariance that make the MVE so attractive. Rousseeuw and van Zomeren (1990) used the (p+1)- subset estimator which was modified by Croux and Haesbroeck (1997) to give rise to the averaged (p+1)- subset estimator . This note shows by means of simulations that the averaged (p+1)-subset estimator outperforms the exact estimator as far as finite-sample efficiency is concerned. We also present a new robust estimator for the MVE, closely related to the averaged (p+1)-subset estimator, but yielding a natural ranking of the data. [less ▲]

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See detailMaxbias curves of robust scale estimators based on subranges
Croux, C.; Haesbroeck, Gentiane ULg

in Metrika (2001), 53(2), 101-122

A maxbias curve is a powerful tool to describe the robustness of an estimator. It is an asymptotic concept which tells how much an estimator can change due to a given fraction of contamination. In this ... [more ▼]

A maxbias curve is a powerful tool to describe the robustness of an estimator. It is an asymptotic concept which tells how much an estimator can change due to a given fraction of contamination. In this paper, maxbias curves are computed for some univariate scale estimators based on subranges: trimmed standard deviations, interquantile ranges and the univariate Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) scale estimators. These estimators are intuitively appealing and easy to calculate. Since the bias behavior of scale estimators may differ depending on the type of contamination (outliers or inliers), expressions for both explosion and implosion maxbias curves are given. On the basis of robustness and efficiency arguments, the MCD scale estimator with 25% breakdown point can be recommended for practical use. [less ▲]

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See detailRégression logistique robuste
Croux, Christophe ULg; Haesbroeck, Gentiane ULg

in Droesbeke, J. J.; Lejeune, M.; Saporta, G. (Eds.) Modèles statistiques pour données qualitatives (2001)

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See detailFormation mathématique par la résolution de problèmes
Bair, Jacques ULg; Haesbroeck, Gentiane ULg

Book published by De Boeck Université (2000)

Entre manuel scolaire et traité d'heuristique, illustré de centaines d'exemples variés, significatifs et souvent inédits, cet ouvrage présente une démarche originale de résolution de problèmes ... [more ▼]

Entre manuel scolaire et traité d'heuristique, illustré de centaines d'exemples variés, significatifs et souvent inédits, cet ouvrage présente une démarche originale de résolution de problèmes mathématiques. [less ▲]

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See detailPrincipal component analysis based on robust estimators of the covariance or correlation matrix: Influence functions and efficiencies
Croux, C.; Haesbroeck, Gentiane ULg

in Biometrika (2000), 87(3), 603-618

A robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In this paper we derive the ... [more ▼]

A robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors. The behaviour of several of these estimators is investigated by a simulation study. It turns out that the theoretical results and simulations favour the use of S-estimators, since they combine a high efficiency with appealing robustness properties. [less ▲]

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See detailEstimateurs Robustes pour les Composantes Principales
Croux, Christophe ULg; Haesbroeck, Gentiane ULg

in Proceedings des XXXII Journées de Statistique (2000)

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See detailInfluence function and efficiency of the minimum covariance determinant scatter matrix estimator
Croux, C.; Haesbroeck, Gentiane ULg

in Journal of Multivariate Analysis (1999), 71(2), 161-190

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute ... [more ▼]

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported. (C) 1999 Academic Press AMS 1991 subject classifications: 62F35, 62G35. [less ▲]

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See detailLa formation quantitative des économistes à la lumière de l'évolution des rapports entre les mathématiques et l'économie
Bair, Jacques ULg; Haesbroeck, Gentiane ULg

in Histoire et épistémologie dans l'éducation mathématique: de la maternelle à l'université, Proceedings I (1999)

Dans cet article, on s'efforce de décrire, de comprendre et de justifier l'accroissement progressif des mathématiques dans la formation des économistes; à cet effet, on analyse l'évolution temporelle de ... [more ▼]

Dans cet article, on s'efforce de décrire, de comprendre et de justifier l'accroissement progressif des mathématiques dans la formation des économistes; à cet effet, on analyse l'évolution temporelle de ces deux disciplines. Une attention particulière est portée sur l'enseignement de la finance. [less ▲]

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See detailEmpirical Influence Functions for Robust Principal Components
Croux, Christophe ULg; Haesbroeck, Gentiane ULg

in 1999 Proceedings of the Statistical Computing Section of the American Statistical Association (1999)

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See detailModèles mathématiques en finance
Bair, Jacques ULg; Haesbroeck, Gentiane ULg; Justens, Daniel et al

Book - Presses Ferrer (1998)

L'ouvrage reprend de manière progressive les principaux résultats théoriques nécessaires à une bonne compréhension des produits financiers usuels, en allant de l'intérêt simple aux modèles stochastiques ... [more ▼]

L'ouvrage reprend de manière progressive les principaux résultats théoriques nécessaires à une bonne compréhension des produits financiers usuels, en allant de l'intérêt simple aux modèles stochastiques et chaotiques. [less ▲]

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See detailModélisation : passage d'un problème réel à un problème mathématique
Bair, Jacques ULg; Haesbroeck, Gentiane ULg

in Bulletin de l'APMEP (1998), 418

Cet article présente un modèle relatif à la transformation d'un problème réel en un problème mathématique, puis du passage d'une solution mathématique à une solution réelle. Cette modélisation est ... [more ▼]

Cet article présente un modèle relatif à la transformation d'un problème réel en un problème mathématique, puis du passage d'une solution mathématique à une solution réelle. Cette modélisation est illustrée par des exemples concrets. [less ▲]

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See detailLe chaos
Haesbroeck, Gentiane ULg

in Bair, Jacques; Haesbroeck, Gentiane; Justens, Daniel (Eds.) et al Modèles mathématiques en finance: de l'incohérence à l'incertitude et au chaos (1998)

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See detailEtude statistique sur la perception des problèmes mathématiques dans l'enseignement
Bair, Jacques ULg; Haesbroeck, Gentiane ULg

in Stratégies et medias pédagogiques pour l'apprentissage et l'évaluation dans l'enseignement supérieur (1997)

Dans cette note est présentée une enquête auprès d'étudiants universitaires (en économie et en gestion) confrontés à des problèmes rencontrés dans l'univers économique et pouvant être résolus à l'aide d ... [more ▼]

Dans cette note est présentée une enquête auprès d'étudiants universitaires (en économie et en gestion) confrontés à des problèmes rencontrés dans l'univers économique et pouvant être résolus à l'aide d'outils mathématiques. Les résultats de cette enquête sont analysés statistiquement. [less ▲]

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See detailMonotonous stability for neutral fixed points
Bair, Jacques ULg; Haesbroeck, Gentiane ULg

in Bulletin of the Belgian Mathematical Society Simon Stevin (1997), 4(5), 639-646

We give subtle, simple and precise results about the convergence or the divergence of the sequence (x(n)), where x(j) = f(x(j-1)) for every integer j, when the initial element x(0) is in the neighbourhood ... [more ▼]

We give subtle, simple and precise results about the convergence or the divergence of the sequence (x(n)), where x(j) = f(x(j-1)) for every integer j, when the initial element x(0) is in the neighbourhood of a neutral fixed point, i.e. a point x* such that f(x*) = x* with \f'(x*)\ = 1 (where f is a C-infinity function defined on a subset of R). [less ▲]

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See detailAn Easy Way to Increase the Finite-Sample Efficiency of the Resampled Minimum Volume Ellipsoid Estimator
Croux, Christophe ULg; Haesbroeck, Gentiane ULg

in Computational Statistics & Data Analysis (1997), 25

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 ... [more ▼]

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. [less ▲]

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