Sliced Inverse Regression (SIR) is a promising technique for the purpose of dimension reduction. Several properties of this relatively new method have been examined already, but little attention has been paid to robustness aspects. We show that SIR is very sensitive towards outliers in the data....

In this paper, we consider one-step outlier identification rules for multivariate data-generalizing the concept of so-called a - outlier identifiers_ as presented in Davies and Gather (1993) for the case of univariate samples. We investigate how the finite sample breakdown points of estimators...

The aim of detecting outliers in a multivariate sample can be pursued in different ways. We investigate here the performance of several simultaneous multivariate outlier identification rules based on robust estimators of location and scale. It has been shown that the use of estimators with high...

In investigations on the behaviour of robust estimators, typically their consistency and their asymptotic normality are studied as a necessity. Their rates of convergence, however, are often given less weight. We show here that the rate of convergence of a multivariate robust estimator to its...

In their paper, Davies and Gather (1993) formalized the task of outlier identification, considering also certain performance criteria for outlier identifiers. One of those Criteria, the maximum asymptotic bias, is carried over here to multivariate outlier identifiers. We show how this term...

Sliced inverse regression (SIR) is a clever technique for reducing the dimension of the predictor in regression problems, thus avoiding the curse of dimensionality. There exist many contributions on various aspects of the performance of SIR. Up to now, few attention has been paid to the problem...

The concept of breakdown point was introduced by Hodges (1967) and Hampel (1968, 1971) and still plays an important though at times a controversial role in robust statistics. It has proved most successful in the context of location, scale and regression problems. In this paper we argue that this...

The present method allows to detect outlying observations in data which may be described by a deterministic function plus a stochastic component. This type of functional relationship often occurs in experimental data, in toxicological research, for instance. The Hampel identifier, an outlier...