Two robustness criteria are presented that are applicable to general clustering methods.
Robustness and stability in cluster analysis are not only data dependent, but even cluster …

ML-estimation based on mixtures of Normal distributions is a widely used tool for cluster
analysis. However, a single outlier can make the parameter estimation of at least one of the …

The breakdown value is a popular measure of the robustness of an estimator against
outlying observations. Roughly speaking, it indicates the smallest fraction of contaminants in …

In extending univariate outlier detection methods to higher dimension, various issues arise:
limited visualization methods, inadequacy of marginal methods, lack of a natural order …

This paper presents a simple resistant estimator of multivariate location and dispersion. The
DD plot is a plot of Mahalanobis distances from the classical estimator versus the distances …

The sample mean vector and the sample covariance matrix are the corner stone of the
classical multivariate analysis. They are optimal when the underlying data are normal. They …

In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in
the logistic regression model. We formally prove that the ML-estimator never explodes to …

Deepest regression (DR) is a method for linear regression introduced by PJ Rousseeuw and
M. Hubert (1999, J. Amer. Statis. Assoc. 94, 388–402). The DR method is defined as the fit …

L p–norm weighted depth functions are introduced and the local and global robustness of
these weighted L p–depth functions and their induced multivariate medians are investigated …

Tukey's halfspace median (HM), servicing as the multivariate counterpart of the univariate
median, has been introduced and extensively studied in the literature. It is supposed and …