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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)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)Régression logistique robuste Croux, Christophe ; Haesbroeck, Gentiane in Droesbeke, J. J.; Lejeune, M.; Saporta, G. (Eds.) Modèles statistiques pour données qualitatives (2001) Detailed reference viewed: 31 (7 ULg)Estimateurs Robustes pour les Composantes Principales Croux, Christophe ; Haesbroeck, Gentiane in Proceedings des XXXII Journées de Statistique (2000) Detailed reference viewed: 12 (3 ULg)Empirical Influence Functions for Robust Principal Components Croux, Christophe ; Haesbroeck, Gentiane in 1999 Proceedings of the Statistical Computing Section of the American Statistical Association (1999) Detailed reference viewed: 4 (0 ULg)An Easy Way to Increase the Finite-Sample Efficiency of the Resampled Minimum Volume Ellipsoid Estimator Croux, Christophe ; Haesbroeck, Gentiane 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 ▲] Detailed reference viewed: 24 (5 ULg) |
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