Robust Kalman tracking and smoothing with propagating and non-propagating outliers

A common situation in filtering where classical Kalman filtering does not perform particularly well is tracking in the presence of propagating outliers. This calls for robustness understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. Based on optimality results for distributional-robust Kalman filtering from Ruckdeschel[01,10], we propose new robust recursive filters and smoothers designed for this purpose as well as specialized versions for non-propagating outliers. We apply these procedures in the context of a GPS problem arising in the car industry. To better understand these filters, we study their behavior at stylized outlier patterns (for which they are not designed) and compare them to other approaches for the tracking problem. Finally, in a simulation study we discuss efficiency of our procedures in comparison to competitors.Comment: 27 pages, 12 figures, 2 table

Online Two-stage Exams als Prüfungsmethode in Statistik-Lehrveranstaltungen

Kollaborative Prüfungsszenarien sorgen während der Prüfung durch zusätzliches Feedback für eine weitere Lernerfahrung. Two-stage Exams im Besonderen kombinieren die individuelle Einzelleistung mit Gruppendiskussionen und erlauben es den Studierenden bei Unsicherheit in mehreren Versuchen die richtige Lösung zu erarbeiten. Anhand zweier Statistik-Lehrveranstaltungen wird die Überführung von papierbasierten Einzelprüfungen in Online Two-stage Exams während der Covid-19 Pandemie beschrieben und die Ergebnisse analysiert. Es konnte gezeigt werden, dass die Studierenden in mehrfacher Hinsicht von diesem Format profitieren und noch während der Prüfung ein Lernzuwachs erfolgt

A cross-cultural study on odor-elicited life stage-associations

Associative conceptualization plays an important role in how we perceive and interact with our environment. Particularly odor associations can be highly vivid and often long-lasting due to their close connection with our episodic memory and emotions. Based on the findings of a study conducted in Austria in 2017, this work was carried out to investigate odor-elicited life stage-associations (OELSA) in seven nations and to identify potential similarities and differences in conceptualizing odor impressions across these nations. A total of 1144 adults (aged 21–60) from Austria, Australia, Germany, Switzerland, Thailand, USA, and Vietnam participated in this study. Nine odors (vanilla, orange, lemon, mint, coconut, basil, rose, anise, and hay) were presented to the participants, and they were asked to answer questions about their spontaneous associations with life stages. The results indicate the existence of OELSA in all investigated nations. For example, vanilla was predominantly assigned to children in all nations, while hay was primarily assigned to elder people. While most of the investigated odors were most frequently associated with adults, some significant differences in OELSA were observed between the different nationalities. For instance, mint was more frequently associated with children by Australian participants compared to participants from all other nations, while coconut was more strongly associated with children by the Vietnamese participants compared to all other participants. The results of this study demonstrate the existence of consistent life stage-related associations elicited by certain odors across different nations and cultures and, at the same time points to differences in life stage-related association with certain odors between the nations. Since this work was not designed to identify the reasons for these differences, we can only make assumptions about the potential underlying causes for these behaviors

Analyzing diabetes data

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On robust spectral density estimation

Zsfassung in dt. SpracheIm folgenden befassen wir uns mit der robusten Spektraldichteschätzung und ihrer Anwendung in der Herzratenvariabilitätsanalyse.Da die klassischen Spektraldichteschätzer empfindlich auf Ausreißer reagieren, sind robuste Verfahren von Bedeutung. Daher konzentrieren wir uns auf die robuste Schätzung der Spektraldichtefunktion und stellen verschiedene, bereits existierende, aber auch neue Methoden vor, die robust gegenüber Ausreißern sind.Wir betrachten Spektraldichteschätzer, die auf einer Robustifizierung der Fourier-Transformation und auf der robusten Schätzung der Autokovarianzfunktion basieren.Um allerdings verlässliche Schätzwerte der Spektraldichtefunktion zu erhalten, die unempfindlich gegenüber Ausreißern sind, ist es besser, zuerst die Ausreißer mittels eines geeigneten robusten Verfahrens herauszufiltern und anschließend die Spektraldichtefunktion der bereinigten Zeitreihe zu berechnen.Diese Bereinigung der Daten leistet ein robustifizierter Kalman-Filter.Wir schlagen dafür einen neuen multivariaten ACM-Typ Filter für Zustandsraummodelle vor. Dieser neuen Filter verallgemeinert den ursprünglichen ACM-Typ Filter, der auf eindimensionale Beobachtungen beschränkt ist. Unser neuer Filter wird mit einem weiteren Ansatz, dem gegenwärtig verwendeten rLS-Filter, verglichen.Alle beschriebenden Methoden sind in der Programmiersprache R implementiert und werden mit Hilfe umfangreicher Simulationsstudien miteinander verglichen. Das beste Verfahren wird zur Analyse der Herzratenvariabilität bei Diabetikern mit unterschiedlich schwerer kardiovaskulärer autonomer Neuropathie herangezogen.In the following we deal with robust spectral density estimation and its application to the analysis of heart rate variability.As classical spectral density estimators are sensitive to outlying observations, robustness is an issue. Hence, we focus on the problem of estimating the spectral density function robustly and present different methods, existing and new ones, that are resistant to outliers.We consider spectral density estimators based on robustifying the Fourier transformation and on robust autocovariance estimation.However, in order to get a reliable estimate of the spectral density function, that is insensitive to outlying observations, it turned out that cleaning the time series in a robust way first and calculating the spectral density function afterwards leads to encouraging results.The data-cleaning operation wherein the robustness is introduced, is accomplished by a robustified version of the Kalman filter. We propose a new multivariate approximate conditional-mean (ACM) type filter for state-space models. This new filtering method generalizes the original ACM-type filter which is bound to the univariate setting. We compare our new filtering method to a second approach, the currently used rLS filter, which is also described.All presented methods are implemented in the open source language R and compared by extensive simulation studies. The most competitive method is also applied to actual heart rate variability data of diabetic patients with different degrees of cardiovascular autonomic neuropathy.12