It is well-known that k-step M-estimators can yield a high efficiency without losing the breakdown point of the initial estimator. In this note we derive their bias curves. In the location framework the bias increases only slightly with k, but in the scale case the bias curves change considerably.

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 infinity, but rather breaks down to zero when adding severe outliers to a data set. An example confirms this behavior.

In the location model there exist M-estimators that combine a 50% breakdown point with an arbitrarily high efficiency. In this article we show that this is also the case for M-estimators of scale at normal models, although all of the well-known M-estimators of scale have a rather low efficiency...

The empirical influence function EIF(x, Tn; X) measures the influence of an observation x on the estimator Tn at a sample X of size n. In this note we show that the empirical influence function of the median is not a consistent estimator of the corresponding influence function. This observation...

In this note we study the problem of estimating the parameters of the conditional median function at elliptical models. For this we use positive-breakdown estimators of multivariate location and scatter, and obtain influence functions and asymptotic variances of the resulting slope and...

This paper presents a new method for robust online variability extraction in time series. The proposed estimator is simultaneously highly robust and efficient. We derive its breakdown point, influence function, and asymptotic variance and study the finite sample properties in a simulation study.