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Comparison of local outliers detection techniques in spatial multivariate data Ernst, Marie ; Haesbroeck, Gentiane E-print/Working paper (2016) Outlier detection techniques in spatial data should allow to identify two types of outliers: global and local ones. Local outliers typically have non-spatial attributes that strongly differ from those ... [more ▼] Outlier detection techniques in spatial data should allow to identify two types of outliers: global and local ones. Local outliers typically have non-spatial attributes that strongly differ from those observed on their neighbors. Detecting local outliers requires to be able to work locally, on neighborhoods, in order to take into account the spatial dependence between the statistical units under consideration, even though the outlyingness is usually measured on the non-spatial variables. Many procedures have been outlined in the literature, but their number reduces when one wants to deal with multivariate non-spatial attributes. In this paper, focus is on the multivariate context. A review of existing procedures is done. A new approach, based on a two-step improvement of an existing one, is also designed and compared with the benchmarked methods by means of examples and simulations. [less ▲] Detailed reference viewed: 39 (18 ULg)Spatial autocorrelation: robustness of measures and tests Ernst, Marie ; Haesbroeck, Gentiane Conference (2015, December 14) Distinguishing the analysis of spatial data from classical analysis is only meaningful if the spatial components bring information. Therefore, testing if the spatial autocorrelation is significant may ... [more ▼] Distinguishing the analysis of spatial data from classical analysis is only meaningful if the spatial components bring information. Therefore, testing if the spatial autocorrelation is significant may confirm or deny the need to consider spatial analysis over the classical one. Spatial autocorrelation expresses the dependence between values at neighbouring locations. Several measures of spatial autocorrelation are defined in the literature. Moran’s index, Geary’s ratio and Getis-Ord statistic are the most used statistics. Tests based on these measures have been developed in the literature using asymptotic and permutation results. They are used in practice in many fields, for instance in geography, economics, biogeosciences, medicine, ... However, these tests should be cautiously applied because they are not robust. A single contaminated observation can significantly modify their results. The talk has two main objectives. Firstly, the already available tools for measuring spatial autocorrelation will be reviewed with an emphasis on the study and comparison of their robustness. Secondly, alternative methods will be proposed to robustly estimate the spatial autocorrelation. [less ▲] Detailed reference viewed: 33 (6 ULg)Multivariate coefficients of variation: a full inference toolbox Aerts, Stéphanie ; Haesbroeck, Gentiane Conference (2015, December 13) The univariate coefficient of variation (CV) is a widely used measure to compare the relative dispersion of a variable in several populations. When the comparison is based on $p$ characteristics however ... [more ▼] The univariate coefficient of variation (CV) is a widely used measure to compare the relative dispersion of a variable in several populations. When the comparison is based on $p$ characteristics however, side-by-side comparison of marginal CV's may lead to contradictions. Several multivariate coefficients of variation (MCV) have been introduced and used in the literature but, so far, their properties have not been much studied. Based on one of them, i.e. the inverse of the Mahalanobis distance between the mean and the origin, this talk intends to demonstrate the usefulness of MCV's in several domains (finance and analytical chemistry) as well as provide a complete inference toolbox for practitioners. Some exact and approximate confidence intervals are constructed, whose performance is analyzed through simulations. Several bias-correction methods, either parametric or not, are suggested and compared. Finally, since MCV's are used for comparison purposes, some test statistics are proposed for the homogeneity of MCV's in $K$ populations. Throughout the talk, the robustness of the techniques will be discussed. As a by-product, a test statistic allowing to reliably compare $K$ univariate CV's even in presence of outliers will be outlined. [less ▲] Detailed reference viewed: 12 (1 ULg)Les mathématiques à l’honneur à MT180 Favart, Evelyne ; Haesbroeck, Gentiane ; Kreusch, Marie Article for general public (2015) Detailed reference viewed: 18 (5 ULg)Multivariate coefficients of variation: Comparison and influence functions Aerts, Stéphanie ; Haesbroeck, Gentiane ; Ruwet, Christel in Journal of Multivariate Analysis (2015), 142 In the univariate setting, coeﬃcients of variation are well-known and used to compare the variability of populations characterized by variables expressed in diﬀerent units or having really diﬀerent means ... [more ▼] In the univariate setting, coeﬃcients of variation are well-known and used to compare the variability of populations characterized by variables expressed in diﬀerent units or having really diﬀerent means. When dealing with more than one variable, the use of such a relative dispersion measure is much less common even though several generalizations of the coeﬃcient of variation to the multivariate setting have been introduced in the literature. In this paper, the lack of robustness of the sample versions of the multivariate coeﬃcients of variation (MCV) is illustrated by means of inﬂuence functions and some robust counterparts based either on the Minimum Covariance Determinant (MCD) estimator or on the S estimator are advocated. Then, focusing on two of the considered MCV’s, a diagnostic tool is derived and its eﬃciency in detecting observations having an unduly large eﬀect on variability is illustrated on a real-life data set. The inﬂuence functions are also used to compute asymptotic variances under elliptical distributions, yielding approximate conﬁdence intervals. Finally, simulations are conducted in order to compare, in a ﬁnite sample setting, the performance of the classical and robust MCV’s in terms of variability and in terms of coverage probability of the corresponding asymptotic conﬁdence intervals. [less ▲] Detailed reference viewed: 97 (28 ULg)The utility of Google Scholar when searching geographical literature: comparison with three commercial bibliographic databases Stirbu, Simona ; Thirion, Paul ; Schmitz, Serge et al in Journal of Academic Librarianship (2015), 41(3), 322-329 This study aims to highlight what benefits, if any, Google Scholar (GS) has for academic literature searches in the field of geography, compared to three commercial bibliographic databases: Web of Science ... [more ▼] This study aims to highlight what benefits, if any, Google Scholar (GS) has for academic literature searches in the field of geography, compared to three commercial bibliographic databases: Web of Science (WoS) and FRANCIS (multidisciplinary databases) and GeoRef (specialized in geosciences). To ensure a valid comparison, identical bibliographic searches were applied using each of the four bibliographic tools. To exclude automatic variations of the ten keywords tested, they were placed between quotation marks and searched only in the “title” field of the respective search tools’ interfaces. The results were limited to bibliographic references published from 2005 to 2009. In order to assess the repeatability of the results, the exact same process was repeated monthly between November 2010 and July 2011. Initially the whole set of results was analyzed, after which the search results for two keywords (selected since they yielded a manageable number of results) were studied in more detail. The results indicate that GS search results show a large degree of overlap with those of the other databases but, moreover, yield numerous unique hits, which should be useful to researchers in both the fields of human and physical geography. GS leads the other tools widely on number of results, independently of keyword, subfield, year of publication, or time of search. [less ▲] Detailed reference viewed: 180 (82 ULg)Doc'Data: mesure de la persévérance au doctorat à l'Université de Liège Aerts, Stéphanie ; Haesbroeck, Gentiane ; Schyns, Michael Report (2015) Le Conseil du Doctorat a parmi ses missions celle d’accompagner les doctorants dans leur parcours et de mettre en place des actions en vue de favoriser la réussite. Cependant, pour réellement mesurer ... [more ▼] Le Conseil du Doctorat a parmi ses missions celle d’accompagner les doctorants dans leur parcours et de mettre en place des actions en vue de favoriser la réussite. Cependant, pour réellement mesurer l’impact des actions mises en oeuvre dans cette optique, il faut d’abord pouvoir quantiﬁer le taux de réussite. Or, mesurer le taux de réussite dans les études de 3ème cycle n’est pas une démarche évidente. De nombreux raccourcis de raisonnement sont tentants mais mènent à des résultats très variables et incorrects. Le but de ce document est de présenter les diﬃcultés inhérentes au calcul d’un taux de réussite et de proposer quelques procédures appropriées. Dans un premier temps, les chances (ou, d’un point de vue plus formel, les probabilités) de réussite et d'abandon des doctorants sont modélisées en fonction du nombre d’années d’inscription et en tenant compte de caractéristiques du doctorant comme son genre, sa nationalité, son âge au moment de l’inscription, son statut professionnel... L'analyse descriptive et exploratoire est ensuite conﬁrmée par l’application d’une analyse de survie avec risques compétitifs. [less ▲] Detailed reference viewed: 97 (57 ULg)Comparison of robust detection techniques for local outliers in multivariate spatial data Ernst, Marie ; Haesbroeck, Gentiane Conference (2014, August 22) Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Spatial data may contain two types of atypical observations: global ... [more ▼] Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Spatial data may contain two types of atypical observations: global and/or local outliers. The attribute values of a global outlier are outlying with respect to the values taken by the majority of the data points while the attribute values of a local outlier are extreme when compared to those of its neighbors. Usual outlier detection techniques may be used to find global outliers as the geographical positions of the data is not taken into account in this specific search. The detection of local outliers is more complex, especially when there are more than one non spatial attributes. This talk focuses on local detection with two main objectives. First, we will shortly review some of the local detection techniques that seem to perform well in practice. Among these, one can find robust ``Mahalanobis-type'' detection techniques and a wheighted PCA approach. We suggest an adaptation to one of these to further develop its local characteristic. Then, examples and simulations, based on linear model of co-regionalisation with Matern models, are reported and discussed in order to compare in an objective way the different detection techniques. [less ▲] Detailed reference viewed: 76 (13 ULg)Robustness and efficiency of multivariate coefficients of variation Aerts, Stéphanie ; Haesbroeck, Gentiane ; Ruwet, Christel Conference (2014, August 12) The coefficient of variation is a well-known measure used in many fields to compare the variability of a variable in several populations. However, when the dimension is greater than one, comparing the ... [more ▼] The coefficient of variation is a well-known measure used in many fields to compare the variability of a variable in several populations. However, when the dimension is greater than one, comparing the variability only marginally may lead to controversial results. Several multivariate extensions of the univariate coefficient of variation have been introduced in the literature. In practice, these coefficients can be estimated by using any pair of location and covariance estimators. However, as soon as the classical mean and covariance matrix are under consideration, the influence functions are unbounded, while the use of any robust estimators yields bounded influence functions. While useful in their own right, the influence functions of the multivariate coefficients of variation are further exploited in this talk to derive a general expression for the corresponding asymptotic variances under elliptical symmetry. Then, focusing on two of the considered multivariate coefficients, a diagnostic tool based on their influence functions is derived and compared, on a real-life dataset, with the usual distance-plot. [less ▲] Detailed reference viewed: 53 (16 ULg)Eugène Catalan Bair, Jacques ; Haesbroeck, Gentiane in Tangente (2014), 158 Eugène Catalan est né il y a exactement 200 ans ! Ses travaux mathématiques sont remarquables, tant par leur quantité (on dénombre environ 380 articles et 70 livres ou mémoires) que du point de vue de ... [more ▼] Eugène Catalan est né il y a exactement 200 ans ! Ses travaux mathématiques sont remarquables, tant par leur quantité (on dénombre environ 380 articles et 70 livres ou mémoires) que du point de vue de leur qualité et de leur variété. En effet, son nom est encore aujourd'hui associé à de nombreux domaines des mathématiques. Citons notamment diverses conjectures fameuses sur les nombres ou équations, l'étude de nombres éponymes en combinatoire, l'introduction des polyèdres semi-réguliers ou des surfaces minimales en géométrie, le calcul d'intégrales multiples ou encore de séries en analyse. A l'occasion de cet anniversaire, nous mettons en évidence quelques éléments de sa biographie. [less ▲] Detailed reference viewed: 30 (5 ULg)Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation Aerts, Stéphanie ; Haesbroeck, Gentiane ; Ruwet, Christel E-print/Working paper (2014) Detailed reference viewed: 60 (26 ULg)Robust detection techniques for multivariate spatial data Ernst, Marie ; Haesbroeck, Gentiane Poster (2013, November 26) Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Two types of atypical observations can be defined: global and/or local ... [more ▼] Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Two types of atypical observations can be defined: global and/or local outliers. The attribute values of a global outlier are outlying with respect to the values taken by the majority of the data points while the attribute values of a local outlier are extreme when compared to those of its neighbors. Classical outlier detection techniques may be used to find global outliers as the geographical positions of the data is not taken into account in this search. The detection of local outliers is more complex especially when there are more than one non spatial attribute. In this poster, two new procedures for local outliers detection are defined. The first approach is to adapt an existing technique using in particular a regularized estimator of the covariance matrix. The second technique measures outlyingness using depth function. [less ▲] Detailed reference viewed: 20 (8 ULg)Detection of Local and Global Outliers in Spatial Data Ernst, Marie ; Haesbroeck, Gentiane Conference (2013, July 11) Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Two types of atypical observations can be defined: global and/or local ... [more ▼] Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Two types of atypical observations can be defined: global and/or local outliers. The attribute values of a global outlier are outlying with respect to the values taken by the majority of the data points while the attribute values of a local outlier are extreme when compared to those of its neighbors. Classical outlier detection techniques may be used to find global outliers as the geographical positions of the data is not taken into account in this search. The detection of local outliers is more complex especially when there are more than one non spatial attribute. In this talk, existing techniques were outlined and two new procedures were defined. The first approach is to adapt an existing technique using in particular a regularized estimator of the covariance matrix. The second technique measures outlyingness using depth function. [less ▲] Detailed reference viewed: 73 (26 ULg)Prix Nobel d'Economie et mathématiques Bair, Jacques ; Haesbroeck, Gentiane in Losanges (2013), 20 Le Prix Nobel d'Economie 2012 a été décerné aux deux mathématiciens américains Lloyd Shapley et Alvin Roth. Cet événement nous a donné l'occasion de nous pencher quelque peu sur des prix internationaux ... [more ▼] Le Prix Nobel d'Economie 2012 a été décerné aux deux mathématiciens américains Lloyd Shapley et Alvin Roth. Cet événement nous a donné l'occasion de nous pencher quelque peu sur des prix internationaux pouvant être attribués à des mathématiciens. [less ▲] Detailed reference viewed: 56 (9 ULg)Classification performance resulting from of 2-means Ruwet, Christel ; Haesbroeck, Gentiane in Journal of Statistical Planning & Inference (2013), 143(2), 408-418 The k-means procedure is probably one of the most common nonhierachical clustering techniques. From a theoretical point of view, it is related to the search for the k principal points of the underlying ... [more ▼] The k-means procedure is probably one of the most common nonhierachical clustering techniques. From a theoretical point of view, it is related to the search for the k principal points of the underlying distribution. In this paper, the classification resulting from that procedure for k=2 is shown to be optimal under a balanced mixture of two spherically symmetric and homoscedastic distributions. Then, the classification efficiency of the 2-means rule is assessed using the second order influence function and compared to the classification efficiencies of the Fisher and logistic discriminations. Influence functions are also considered here to compare the robustness to infinitesimal contamination of the 2-means method w.r.t. the generalized 2-means technique. [less ▲] Detailed reference viewed: 78 (18 ULg)Robust estimation for ordinal regression Croux, Christophe ; Haesbroeck, Gentiane ; Ruwet, Christel in Journal of Statistical Planning & Inference (2013), 143(9), 14861499 Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum ... [more ▼] Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot. [less ▲] Detailed reference viewed: 29 (7 ULg)Modèles chaotiques en économie Bair, Jacques ; Haesbroeck, Gentiane in Tangente Sup (2012), 63 - 64 Dans cet ouvrage consacré au thème des prévisions, nous montrons que certains modèles mathématiques ,reposant sur des équations récurrentes non linéaires, permettent de décrire des phénomènes qui ... [more ▼] Dans cet ouvrage consacré au thème des prévisions, nous montrons que certains modèles mathématiques ,reposant sur des équations récurrentes non linéaires, permettent de décrire des phénomènes qui paraissent aléatoires, alors qu'ils sont purement déterministes. Une application à l'économie illustre les propos. [less ▲] Detailed reference viewed: 79 (10 ULg)Impact of contamination on training and test error rates in statistical clustering Ruwet, Christel ; Haesbroeck, Gentiane in Communications in Statistics : Simulation & Computation (2011), 40(3), 394-411 The k-means algorithm is one of the most common nonhierarchical methods of clustering. It aims to construct clusters in order to minimize the within cluster sum of squared distances. However, as most ... [more ▼] The k-means algorithm is one of the most common nonhierarchical methods of clustering. It aims to construct clusters in order to minimize the within cluster sum of squared distances. However, as most estimators defined in terms of objective functions depending on global sums of squares, the k-means procedure is not robust with respect to atypical observations in the data. Alternative techniques have thus been introduced in the literature, e.g. the k-medoids method. The k-means and k-medoids methodologies are particular cases of the generalized k-means procedure. In this paper, focus is on the error rate these clustering procedures achieve when one expects the data to be distributed according to a mixture distribution. Two different definitions of the error rate are under consideration, depending on the data at hand. It is shown that contamination may make one of these two error rates decrease even under optimal models. The consequence of this will be emphasized with the comparison of influence functions and breakdown points of these error rates. [less ▲] Detailed reference viewed: 117 (44 ULg)Robustness in ordinal regression Ruwet, Christel ; Haesbroeck, Gentiane ; Conference (2010, October 14) Logistic regression is a widely used tool designed to model the success probability of a Bernoulli random variable depending on some explanatory variables. A generalization of this bimodal model is the ... [more ▼] Logistic regression is a widely used tool designed to model the success probability of a Bernoulli random variable depending on some explanatory variables. A generalization of this bimodal model is the multinomial case where the dependent variable has more than two categories. When these categories are naturally ordered (e.g. in questionnaires where individuals are asked whether they strongly disagree, disagree, are indifferent, agree or strongly agree with a given statement), one speaks about ordered or ordinal regression. The classical technique for estimating the unknown parameters is based on Maximum Likelihood estimation (e.g. Powers and Xie, 2008 or Agresti, 2002). However, as Albert and Anderson (1984) showed in the binary context, Maximum Likelihood estimates sometimes do not exist. Existence conditions in the ordinal setting, derived by Haberman in a discussion of McCullagh’s paper (1980), as well as a procedure to verify that they are fulfilled on a particular dataset will be presented. On the other hand, Maximum Likelihood procedures are known to be vulnerable to contamination in the data. The lack of robustness of this technique in the simple logistic regression setting has already been investigated in the literature (e.g. Croux et al., 2002 or Croux et al., 2008). The breakdown behaviour of the ML-estimation procedure will be considered in the context of ordinal logistic regression. A robust alternative based on a weighting idea will then be suggested and compared to the classical one by means of their influence functions. Influence functions can be used to construct a diagnostic plot allowing to detect influential observation for the classical ML procedure (Pison and Van Aelst, 2004). [less ▲] Detailed reference viewed: 54 (10 ULg)Robust ordinal logistic regression Ruwet, Christel ; Haesbroeck, Gentiane ; Croux, Christophe Conference (2010, June 28) Logistic regression is a widely used tool designed to model the success probability of a Bernoulli random variable depending on some explanatory variables. A generalization of this bimodal model is the ... [more ▼] Logistic regression is a widely used tool designed to model the success probability of a Bernoulli random variable depending on some explanatory variables. A generalization of this bimodal model is the multinomial case where the dependent variable has more than two categories. When these categories are naturally ordered (e.g. in questionnaires where individuals are asked whether they strongly disagree, disagree, are indifferent, agree or strongly agree with a given statement), one speaks about ordered or ordinal logistic regression. The classical technique for estimating the unknown parameters is based on Maximum Likelihood estimation. Maximum Likelihood procedures are however known to be vulnerable to contamination in the data. The lack of robustness of this technique in the simple logistic regression setting has already been investigated in the literature, either by computing breakdown points or influence functions. Robust alternatives have also been constructed for that model. In this talk, the breakdown behaviour of the ML-estimation procedure will be considered in the context of ordinal logistic regression. Influence functions will be computed and shown to be unbounded. A robust alternative based on a weighting idea will then be suggested and illustrated on some examples. The influence functions of the ordinal logistic regression estimators may be used to compute classification efficiencies or to derive diagnostic measures, as will be illustrated on some examples. [less ▲] Detailed reference viewed: 109 (14 ULg) |
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