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...

Quadratic covariation is a popular descriptive measure for the volatility of a multivariate price process. It is consistently estimated by the sum of outer products of high-frequency returns. The proposed realized outlyingness weighted covariation (ROWCov) is a weighted sum of outer products of...

This paper presents variance extraction procedures for univariate time series. The volatility of a times series is monitored allowing for non-linearities, jumps and outliers in the level. The volatility is measured using the height of triangles formed by consecutive observations of the time...