Multivariate Appoximations to Portfolio Return Distribution

This article proposes a three-step procedure to estimate portfolio return distributions under the multivariate Gram-Charlier (MGC) distribution. The method combines quasi maximum likelihood (QML) estimation for conditional means and variances and the method of moments (MM) estimation for the rest of the density parameters, including the correlation coefficients. The procedure involves consistent estimates even under density misspecification and solves the so-called ‘curse of dimensionality’ of multivariate modelling. Furthermore, the use of a MGC distribution represents a flexible and general approximation to the true distribution of portfolio returns and accounts for all its empirical regularities. An application of such procedure is performed for a portfolio composed of three European indices as an illustration. The MM estimation of the MGC (MGC-MM) is compared with the traditional maximum likelihood of both the MGC and multivariate Student’s t (benchmark) densities. A simulation on Value-at-Risk (VaR) performance for an equally weighted portfolio at 1% and 5% confidence indicates that the MGC-MM method provides reasonable approximations to the true empirical VaR. Therefore, the procedure seems to be a useful tool for risk managers and practitioners.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Multivariate analysis of regional-scale geochemical data for environmental monitoring

A compositional multivariate approach is used to analyse regional scale soil geochemical data obtained as part of the Tellus Project generated by the Geological Survey Northern Ireland (GSNI). The multi-element total concentration data presented comprise XRF analyses of 6862 rural soil samples collected at 20cm depths on a non-aligned grid at one site per 2 km2. Censored data were imputed using published detection limits. Using these imputed values for 46 elements (including LOI), each soil sample site was assigned to the regional geology map provided by GSNI initially using the dominant lithology for the map polygon. Northern Ireland includes a diversity of geology representing a stratigraphic record from the Mesoproterozoic, up to and including the Palaeogene. However, the advance of ice sheets and their meltwaters over the last 100,000 years has left at least 80% of the bedrock covered by superficial deposits, including glacial till and post-glacial alluvium and peat. The question is to what extent the soil geochemistry reflects the underlying geology or superficial deposits. To address this, the geochemical data were transformed using centered log ratios (clr) to observe the requirements of compositional data analysis and avoid closure issues. Following this, compositional multivariate techniques including compositional Principal Component Analysis (PCA) and minimum/maximum autocorrelation factor (MAF) analysis method were used to determine the influence of underlying geology on the soil geochemistry signature. PCA showed that 72% of the variation was determined by the first four principal components (PC’s) implying “significant” structure in the data. Analysis of variance showed that only 10 PC’s were necessary to classify the soil geochemical data. To consider an improvement over PCA that uses the spatial relationships of the data, a classification based on MAF analysis was undertaken using the first 6 dominant factors. Understanding the relationship between soil geochemistry and superficial deposits is important for environmental monitoring of fragile ecosystems such as peat. To explore whether peat cover could be predicted from the classification, the lithology designation was adapted to include the presence of peat, based on GSNI superficial deposit polygons and linear discriminant analysis (LDA) undertaken. Prediction accuracy for LDA classification improved from 60.98% based on PCA using 10 principal components to 64.73% using MAF based on the 6 most dominant factors. The misclassification of peat may reflect degradation of peat covered areas since the creation of superficial deposit classification. Further work will examine the influence of underlying lithologies on elemental concentrations in peat composition and the effect of this in classification analysis.

Adaption bekannter Lean-Methoden auf die Anforderungen einer mehrstufigen Teilefertigung

Otto-von Guericke-Universität Magdeburg, Fakultät für Maschinenbau, Dissertation, 2016

Multivariate statistical modeling of an anode backing furnace - Modélisation statistique multivariée du four à cuisson des anodes utilisées dans la fabrication d'aluminium primaire

La stratégie actuelle de contrôle de la qualité de l’anode est inadéquate pour détecter les anodes défectueuses avant qu’elles ne soient installées dans les cuves d’électrolyse. Des travaux antérieurs ont porté sur la modélisation du procédé de fabrication des anodes afin de prédire leurs propriétés directement après la cuisson en utilisant des méthodes statistiques multivariées. La stratégie de carottage des anodes utilisée à l’usine partenaire fait en sorte que ce modèle ne peut être utilisé que pour prédire les propriétés des anodes cuites aux positions les plus chaudes et les plus froides du four à cuire. Le travail actuel propose une stratégie pour considérer l’histoire thermique des anodes cuites à n’importe quelle position et permettre de prédire leurs propriétés. Il est montré qu’en combinant des variables binaires pour définir l’alvéole et la position de cuisson avec les données routinières mesurées sur le four à cuire, les profils de température des anodes cuites à différentes positions peuvent être prédits. Également, ces données ont été incluses dans le modèle pour la prédiction des propriétés des anodes. Les résultats de prédiction ont été validés en effectuant du carottage supplémentaire et les performances du modèle sont concluantes pour la densité apparente et réelle, la force de compression, la réactivité à l’air et le Lc et ce peu importe la position de cuisson.

Friederike Heinzel: Methoden der Kindheitsforschung, Ein Überblick über Forschungszugänge zur kindlichen Perspektive. Weinheim / Basel: Beltz Juventa 2012 [Rezension]

Rezension von: Friederike Heinzel: Methoden der Kindheitsforschung, Ein Überblick über Forschungszugänge zur kindlichen Perspektive, Weinheim / Basel: Beltz Juventa 2012 (388 S.; ISBN 978-3-7799-1553-9; 34,95 EUR)

Ein Ansatz zur methoden- und werkzeuggestützten Anforderungs- und Systemspezifikation auf der Grundlage objektorientierter Modellierungs- und Simulationstechniken

Vorgestellt wird ein Ansatz zur objektorientierten Modellierung, Simulation und Animation von Informationssystemen. Es wird ein Vorgehensmodell dargestellt, mit dem unter Verwendung des beschriebenen Ansatzes Anforderungs- oder Systemspezifikationen von Rechnergestützten Informationssystemen erstellt werden können. Der Ansatz basiert auf einem Metamodell zur Beschreibung Rechnergestützter Informationssysteme und verfügt über eine rechnergestützte Modellierungsumgebung. Anhand eines Projektes zur Entwicklung einer Anforderungsspezifikation für ein rechnergestütztes Pflegedokumentations- und -kommunikationssystems wird der Einsatz der Methode beispielhaft illustriert.

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.

Karin Bock / Ingrid Miethe (Hrsg.): Handbuch Qualitative Methoden in der Sozialen Arbeit. Opladen: Barbara Budrich 2010 [Rezension]

Rezension von: Karin Bock / Ingrid Miethe (Hrsg.): Handbuch Qualitative Methoden in der Sozialen Arbeit. Opladen: Barbara Budrich 2010 (711 S.; ISBN 978-3-8664-9255-4)

Bernhard Bonz: Methoden der Berufsbildung, Ein Lehrbuch. Stuttgart: Hirzel 2009 [Rezension]

Rezension von: Bernhard Bonz: Methoden der Berufsbildung, Ein Lehrbuch, Stuttgart: Hirzel 2009 (280 S.; ISBN 978-3-7776-1528-8)