The vector autoregressive model is very popular for modeling multiple time series.Estimation of its parameters is done by a least squares procedure. However, this estimation method is unreliable when outliers are present in the data, and there is a need for robust alternatives. In this paper we propose to estimate the vector autoregressive model by using a trimmed least squares estimator. We show how the order of the autoregressive model can be determined in a robust way, and how confidence bounds around the robustly estimated impulse response functions can be constructed. The resistance of the estimators to outliers is studied on real and simulated data.

In this paper it is studied how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the performance of the associated classification rule. Focus is on the effect of outliers on the misclassification rate, merely than on the estimates of the parameters of the quadratic discriminant rule. The expression for the partial influence function is then used to construct a diagnostic tool for detecting influential observations. Applications on real data sets are provided.

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Logistic regression is frequently used for classifying observations into two groups. Unfortunately there are often outlying observations in a data set and these might affect the estimated model and the associated classification error rate. In this paper, the authors study the effect of observations in the training sample on the error rate by deriving influence functions. They obtain a general expression for the influence function of the error rate, and they compute it for the maximum likelihood estimator as well as for several robust logistic discrimination procedures. Besides being of interest in their own right, the influence functions are also used to derive asymptotic classification efficiencies of different logistic discrimination rules.The authors also show how influential points can be detected by means of a diagnostic plot based on the values of the influence function.Discrimination logistique robuste : approche fondee sur la notion de fonction d'influence R b u d : La rtgression logistique est souvent employ& pour rtpartir des observations entre deux groupes. Les observations atypiques, assez fresuentes en analyse de donntes, peuvent toutefois influer sur l'ajustement du modkle et sur le taux d'erreur correspondant. Dans cet article, les auteurs font appel h la notion de fonction d'influence pour mesurer l'impact que les observations de 1'6chantillon de travail pourraient avoir sur le taux d'erreur. 11s dtterminent la fonction d'influence du taux d'erreur en toute gtntralitd et ils en illustrent le calcul dans le cas de l'estimateur h vraisemblance maximale et de plusieurs proctdures de discrimination logistique robustes. Au-delh de son inttrst intrindque, la fonction d'influence permet de comparer diverses r&gles de discrimination logistique par I'intermUaire de leur efficacitt asymptotique de classification. Les auteurs montrent aussi comment mettre en evidence les observations influentes au moyen d'un outil diagnostique graphique dkduit de la fonction d'influence.