Kristel Joossens

Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares Procedure

The vector autoregressive model is very popular for modeling multiple time series. Estimation of its parameters is typically done by a least squares procedure. However, this estimation method is unreliable when outliers are present in the data, and therefore we propose to estimate the vector autoregressive model by using a multivariate least trimmed squares estimator. We also show how the order of the autoregressive model can be determined in a robust way. The robust procedure is illustrated on a real data set.

Multiple group linear discriminant analysis: robustness and error rate

Discriminant analysis for multiple groups is often done using Fisher’s rule, and can be used to classify observations into different populations. In this paper, we measure the performance of classical and robust Fisher discriminant analysis using the Error Rate as a performance criterion.We were able to derive an expression for the optimal error rate in the situation of three groups. This optimal error rate serves then as a benchmark in the simulation experiments.

Logistic discrimination using robust estimators

Logistic regression is frequently used for classifying observations into two groups. Unfortunately there are often outlying observations in a data set, who might affect the estimated model and the associated classification error rate. In this paper, the effect of observations in the training sample on the error rate is studied by computing influence functions. It turns out that the usual influence function vanishes, and that the use of second order influence functions is appropriate. It is shown that using robust estimators in logistic discrimination strongly reduces the effect of outliers on the classification error rate. Furthermore, the second order influence function can be used as diagnostic tool to pinpoint outlying observations.

Robust Linear Discriminant Analysis for Multiple Groups: Influence and Classification Efficiencies

Linear discriminant analysis for multiple groups is typically carried out using Fishers method. This method relies on the sample averages and covariance matrices computed from the different groups constituting the training sample. Since sample averages and covariance matrices are not robust, it is proposed to use robust estimators of location and covariance instead, yielding a robust version of Fishers method. In this paper expressions are derived for the influence that an observation in the training set has on the error rate of the Fisher method for multiple linear discriminant analysis. These influence functions on the error rate turn out to be unbounded for the classical rule, but bounded when using a robust approach. Using these influence functions, we compute relative classification efficiencies of the robust procedures with respect to the classical method. It is shown that, by using an appropriate robust estimator, the loss in classification efficiency at the normal model remains limited. These findings are confirmed by finite sample simulations.