Titlebook: Robustness and Complex Data Structures; Festschrift in Honou Claudia Becker,Roland Fried,Sonja Kuhnt Book 2013 Springer-Verlag Berlin Heide

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Depth Statisticsary point . with respect to the data, David Donoho and Miriam Gasko considered hyperplanes through . and determined its ‘depth’ by the smallest portion of data that are separated by such a hyperplane. Since then, these ideas have proved extremely fruitful. A rich statistical methodology has develope

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Multivariate Extremes: A Conditional Quantile Approach therefore, not straightforward. We use a definition based on the ordering of a multivariate sample according to an increasing family of curves, we have called isobars. For a given level u, a u-level isobar is defined as a level curve of the conditional distribution function of the radius given the

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High-Breakdown Estimators of Multivariate Location and Scatterollow an elliptical distribution with location vector . and positive definite scatter matrix .. Robust methods aim to estimate . and . even though the data has been contaminated by outliers. The well-known multivariate M-estimators can break down when the outlier fraction exceeds 1/(.+1) where . is

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Upper and Lower Bounds for Breakdown Pointsather using algebraic groups of transformations. It is shown that the upper bound for the finite sample breakdown point has a simpler form than for the population breakdown point. This result is applied to multivariate regression. It is shown that the upper bounds of the breakdown points of estimato

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The Concept of ,-Outliers in Structured Data Situationsch are not has been asked. There is a considerable amount of uncertainty and opacity in data analyses where authors claim that certain observations do not fit to the rest of the data and have therefore been removed or analyzed more accurately. However, no unique definition of the term “outlier” exis

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Multivariate Outlier Identification Based on Robust Estimators of Location and Scattertive against so-called outliers, the use of outlier identification methods based on robust statistical estimators is recommended. One class of such robust estimators is constructed according to the principle of subset selection, meaning that an outlier-free subset of the data is identified first whi

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Robustness for Compositional Dataard statistical tools can be applied. Different possible transformations and their properties are discussed. For robust multivariate methods based on a robust covariance estimation, it is crucial to use a transformation that avoids singularity issues. Moreover, the robust location and covariance est

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