On Higher Order Elicitability and Some Limit Theorems on the Poisson and Wiener Space

This PhD thesis consists of two independent parts. The first one is dedicated to a thorough study of higher order elicitability whereas the second part is concerned with qualitative and quantitative limit theorems for Poisson and Gaussian functionals. It comprises a total number of four articles, three of them already published in peer-reviewed journals (Annals of Statistics, Risk Magazine, and ALEA), the fourth one in a preprint version. The articles are accompanied by detailed additional material, primarily concerning questions of order-sensitivity, order-preservingness and convexity of strictly consistent scoring functions

Erratum: Higher order elicitability and Osband's principle.

This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016)

Elicitability of range value at risk

The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring functions should be (strictly) consistent for the functional of interest, that is, the expected score should be minimised by the correctly specified functional value. A functional is elicitable if it possesses a strictly consistent scoring function. In quantitative risk management, the elicitability of a risk measure is closely related to comparative backtesting procedures. As such, it has gained considerable interest in the debate about which risk measure to choose in practice. While this discussion has mainly focused on the dichotomy between Value at Risk (VaR) - a quantile - and Expected Shortfall (ES) - a tail expectation, this paper is concerned with Range Value at Risk (RVaR). RVaR can be regarded as an interpolation of VaR and ES, which constitutes a tradeoff between the sensitivity of the latter and the robustness of the former. Recalling that RVaR is not elicitable, we show that a triplet of RVaR with two VaR components at different levels is elicitable. We characterise the class of strictly consistent scoring functions. Moreover, additional properties of these scoring functions are examined, including the diagnostic tool of Murphy diagrams. The results are illustrated with a simulation study, and we put our approach in perspective with respect to the classical approach of trimmed least squares in robust regression

Brief training in mindfulness may normalize a blunted error-related negativity in chronically depressed patients

This is the final version of the article. Available from the publisher via the DOI in this record.The error-related negativity (ERN), an evoked-potential that arises in response to the commission of errors, is an important early indicator of self-regulatory capacities. In this study we investigated whether brief mindfulness training can reverse ERN deficits in chronically depressed patients. The ERN was assessed in a sustained attention task. Chronically depressed patients (n = 59) showed significantly blunted expression of the ERN in frontocentral and frontal regions, relative to healthy controls (n = 18). Following two weeks of training, the patients (n = 24) in the mindfulness condition showed a significantly increased ERN magnitude in the frontal region, but there were no significant changes in patients who had received a resting control (n = 22). The findings suggest that brief training in mindfulness may help normalize aberrations in the ERN in chronically depressed patients, providing preliminary evidence for the responsiveness of this parameter to mental training.This research was funded by German Research Foundation Grant No. BA2255 3-1, awarded to T.B. T.B. was also supported by a Heisenberg Fellowship from the German Research Foundation (BA2255 2-1

Physical activity to improve cognition in older adults: can physical activity programs enriched with cognitive challenges enhance the effects? A systematic review and meta-analysis

: EPHPP quality rating scores (DOCX 38 kb

Non-verbal IQ Gains from Relational Operant Training Explain Variance in Educational Attainment: An Active-Controlled Feasibility Study

Research suggests that training relational operant patterns of behavior can lead to increases in general cognitive ability and educational outcomes. Most studies to date have been under-powered and included proxy measures of educational attainment. We attempted to extend previous findings with increased experimental control in younger children (aged 6.9–10.1 years). Participants (N = 49) were assigned to either a relational training or chess control group. Over 5 months, teachers assigned class time to complete either relational training or play chess. Those who were assigned relational training gained 8.9 non-verbal IQ (NVIQ) points, while those in the control condition recorded no gains (dppc2 = .99). Regression analyses revealed that post-training NVIQ predicted reading test scores (conducted approximately 1 month later) over and above baseline NVIQ in the experimental condition only, consistent with what we might expect in a full test of far transfer towards educational outcomes

Order-Sensitivity and Equivariance of Scoring Functions

The relative performance of competing point forecasts is usually measured in terms of loss or scoring functions. It is widely accepted that these scoring function should be strictly consistent in the sense that the expected score is minimized by the correctly specified forecast for a certain statistical functional such as the mean, median, or a certain risk measure. Thus, strict consistency opens the way to meaningful forecast comparison, but is also important in regression and M-estimation. Usually strictly consistent scoring functions for an elicitable functional are not unique. To give guidance on the choice of a scoring function, this paper introduces two additional quality criteria. Order-sensitivity opens the possibility to compare two deliberately misspecified forecasts given that the forecasts are ordered in a certain sense. On the other hand, equivariant scoring functions obey similar equivariance properties as the functional at hand - such as translation invariance or positive homogeneity. In our study, we consider scoring functions for popular functionals, putting special emphasis on vector-valued functionals, e.g. the pair (mean, variance) or (Value at Risk, Expected Shortfall)

Testing the maximal rank of the volatility process for continuous diffusions observed with noise

In this paper, we present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high frequency observations, we construct a test statistic for the maximal rank of the time varying stochastic volatility process. Our methodology is based upon a combination of a matrix perturbation approach and pre-averaging. We will show the asymptotic mixed normality of the test statistic and obtain a consistent testing procedure. We complement the paper with a simulation and an empirical study showing the performances on finite samples