Varianzanalysen - Prüfen der Voraussetzungen und nichtparametrische Methoden sowie praktische Anwendungen mit R und SPSS. Version 1.1 (2.3.2015)

Die Voraussetzunen der parametrischen 1- und mehrfaktoriellen Varianzanalyse, mit und ohne Messwiederholungen, werden besprochen. Ferner werden eine Reihe von alternativen Verfahren vorgestellt, insbesondere einige nichtparametrische, darunter RT (rank transform), INT (inverse normal transform), ART (aligned rank transform), Puri & Sen (L statistic), van der Waerden und Akritas & Brunner (ATS anova type statistic), die sich auf die parametrische Varianzanalyse zurückführen lassen, sowie dichotome und ordinale logistische Regression. Hierzu werden Lösungen mit R und SPSS ausführlich gezeigt.

Geometrical Methods in Multivariate Risk Management: Algorithms and Applications

This thesis builds a framework for evaluating downside risk from multivariate data via a special class of risk measures (RM). The peculiarity of the analysis lies in getting rid of strong data distributional assumptions and in orientation towards the most critical data in risk management: those with asymmetries and heavy tails. At the same time, under typical assumptions, such as the ellipticity of the data probability distribution, the conformity with classical methods is shown. The constructed class of RM is a multivariate generalization of the coherent distortion RM, which possess valuable properties for a risk manager. The design of the framework is twofold. The first part contains new computational geometry methods for the high-dimensional data. The developed algorithms demonstrate computability of geometrical concepts used for constructing the RM. These concepts bring visuality and simplify interpretation of the RM. The second part develops models for applying the framework to actual problems. The spectrum of applications varies from robust portfolio selection up to broader spheres, such as stochastic conic optimization with risk constraints or supervised machine learning.