Recursive Estimation of Orientation Based on the Bingham Distribution

Directional estimation is a common problem in many tracking applications. Traditional filters such as the Kalman filter perform poorly because they fail to take the periodic nature of the problem into account. We present a recursive filter for directional data based on the Bingham distribution in two dimensions. The proposed filter can be applied to circular filtering problems with 180 degree symmetry, i.e., rotations by 180 degrees cannot be distinguished. It is easily implemented using standard numerical techniques and suitable for real-time applications. The presented approach is extensible to quaternions, which allow tracking arbitrary three-dimensional orientations. We evaluate our filter in a challenging scenario and compare it to a traditional Kalman filtering approach

Dependence modeling with applications in financial econometrics

The amount of data available in banking, finance and economics steadily increases due to the ongoing technological progress and the continuing digitalization. A key element of many econometric models for analyzing this data are methods for assessing dependencies, cross-sectionally as well as intertemporally. For this reason, the thesis is centered around statistical and econometric methods for dependence modeling with applications in financial econometrics. The first part of this cumulative dissertation consists of three contributions. The first contribution provides a thorough explanation of the partial copula. It is a natural generalization of the partial correlation coefficient and several of its properties are investigated. In the second contribution, a different multivariate generalization of the partial correlation, the partial vine copula (PVC), is introduced. The PVC is a specific simplified vine copula (SVC) consisting of bivariate higher-order partial copulas, which are copula-based generalizations of sequentially computed partial correlations. Several properties of the PVC are presented and it is shown that, if SVCs are considered as approximations of multivariate distributions, the PVC has a special role as it is the limit of stepwise estimators. The third contribution introduces statistical tests for the simplifying assumption with a special focus on high-dimensional vine copulas. We propose a computationally feasible test for the simplifying assumption in high-dimensions, which is successfully applied to data sets with up to 49 dimensions. The novel test procedure is based on a decision tree which is used to identify the possibly strongest violation of the simplifying assumption. The asymptotic distribution of the test statistic is derived under consideration of estimation uncertainty in the copula parameters. The finite sample performance is analyzed in an extensive simulation study and the results show that the power of the test only slightly decreases in the dimensionality of the test problem. In the second part of the dissertation, the assessment of risk measures is studied with a special focus on the financial return data used for estimation. It is shown that the choice of the sampling scheme can greatly affect the results of risk assessment procedures if the assessment frequency and forecasting horizon are fixed. Specifically, we study sequences of variance estimates and show that they exhibit spurious seasonality, if the assessment frequency is higher than the sampling frequency of non-overlapping return data. The root cause of spurious seasonality is identified by deriving the theoretical autocorrelation function of sequences of variance estimates under general assumptions. To overcome spurious seasonality, alternative variance estimators based on overlapping return data are suggested. The third part of the dissertation is about state space methods for systems with lagged states in the measurement equation. Recently, a low-dimensional modified Kalman filter and smoother for such systems was proposed in the literature. Special attention is paid to the modified Kalman smoother, for which it is shown that the suggested smoother in general does not minimize the mean squared error (MSE). The correct MSE-minimizing modified Kalman smoother is derived and computationally more efficient smoothing algorithms are discussed. Finally, a comparison of the competing smoothers with regards to the MSE is performed

Unscented Orientation Estimation Based on the Bingham Distribution

Orientation estimation for 3D objects is a common problem that is usually tackled with traditional nonlinear filtering techniques such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). Most of these techniques assume Gaussian distributions to account for system noise and uncertain measurements. This distributional assumption does not consider the periodic nature of pose and orientation uncertainty. We propose a filter that considers the periodicity of the orientation estimation problem in its distributional assumption. This is achieved by making use of the Bingham distribution, which is defined on the hypersphere and thus inherently more suitable to periodic problems. Furthermore, handling of non-trivial system functions is done using deterministic sampling in an efficient way. A deterministic sampling scheme reminiscent of the UKF is proposed for the nonlinear manifold of orientations. It is the first deterministic sampling scheme that truly reflects the nonlinear manifold of the orientation

Dependence modeling with applications in financial econometrics

The amount of data available in banking, finance and economics steadily increases due to the ongoing technological progress and the continuing digitalization. A key element of many econometric models for analyzing this data are methods for assessing dependencies, cross-sectionally as well as intertemporally. For this reason, the thesis is centered around statistical and econometric methods for dependence modeling with applications in financial econometrics. The first part of this cumulative dissertation consists of three contributions. The first contribution provides a thorough explanation of the partial copula. It is a natural generalization of the partial correlation coefficient and several of its properties are investigated. In the second contribution, a different multivariate generalization of the partial correlation, the partial vine copula (PVC), is introduced. The PVC is a specific simplified vine copula (SVC) consisting of bivariate higher-order partial copulas, which are copula-based generalizations of sequentially computed partial correlations. Several properties of the PVC are presented and it is shown that, if SVCs are considered as approximations of multivariate distributions, the PVC has a special role as it is the limit of stepwise estimators. The third contribution introduces statistical tests for the simplifying assumption with a special focus on high-dimensional vine copulas. We propose a computationally feasible test for the simplifying assumption in high-dimensions, which is successfully applied to data sets with up to 49 dimensions. The novel test procedure is based on a decision tree which is used to identify the possibly strongest violation of the simplifying assumption. The asymptotic distribution of the test statistic is derived under consideration of estimation uncertainty in the copula parameters. The finite sample performance is analyzed in an extensive simulation study and the results show that the power of the test only slightly decreases in the dimensionality of the test problem. In the second part of the dissertation, the assessment of risk measures is studied with a special focus on the financial return data used for estimation. It is shown that the choice of the sampling scheme can greatly affect the results of risk assessment procedures if the assessment frequency and forecasting horizon are fixed. Specifically, we study sequences of variance estimates and show that they exhibit spurious seasonality, if the assessment frequency is higher than the sampling frequency of non-overlapping return data. The root cause of spurious seasonality is identified by deriving the theoretical autocorrelation function of sequences of variance estimates under general assumptions. To overcome spurious seasonality, alternative variance estimators based on overlapping return data are suggested. The third part of the dissertation is about state space methods for systems with lagged states in the measurement equation. Recently, a low-dimensional modified Kalman filter and smoother for such systems was proposed in the literature. Special attention is paid to the modified Kalman smoother, for which it is shown that the suggested smoother in general does not minimize the mean squared error (MSE). The correct MSE-minimizing modified Kalman smoother is derived and computationally more efficient smoothing algorithms are discussed. Finally, a comparison of the competing smoothers with regards to the MSE is performed

Comparison of a ceiling-mounted 3D flat panel detector vs. conventional intraoperative 2D fluoroscopy in plate osteosynthesis of distal radius fractures with volar locking plate systems

Methods Using a common volar approach on 12 cadaver forearms, total intraarticular distal radius fractures were induced, manually reduced and internally fixated with a 2.4 distal radius locking compression plate. 2D (anterior-posterior and lateral) and 3D (rotational) fluoroscopic images were taken as well as computed tomographies. Fluoroscopic images, Cone Beam CT (CBCT), 360° rotating sequences (so called "Movies") and CT scans were co-evaluated by a specialist orthopedic surgeon and a specialist radiologist regarding quality of fracture reduction, position of plate, position of the three distal locking screws and position of the three diaphyseal screws. In reference to gold standard CT, sensitivity and specifity were analyzed. Results "Movie" showed highest sensitivity for detection of insufficient fracture reduction (88%). Sensitivity for detection of incorrect position of plate was 100% for CBCT and 90% for "Movie." For intraarticular position of screws, 2D fluoroscopy and CBCT showed highest sensitivity and specifity (100 and 91%, respectively). Regarding detection of only marginal intraarticular position of screws, sensitivity and specifity of 2D fluoroscopy reached 100% (CBCT: 100 and 83%). "Movie" showed highest sensitivity for detection of overlapping position of screws (100%). When it comes to specifity, CBCT achieved 100%. Regarding detection of only marginal overlapping position of screws, 2D fluoroscopy and "Movie" showed highest sensitivity (100%). CBCT achieved highest specifity (100%). Conclusion As for assessment of quality of fracture reduction and detection of incorrect position of plate as well as overlapping position of the three diaphyseal screws CBCT and "Movie" are comparable to CT - especially when combined. Particularly sensitivity is high compared to standard 2D fluoroscopy

ALKBH5-induced demethylation of mono- and dimethylated adenosine

RNA contains methylated A-base derivatives. A methylation to m(6)A and then demethylation regulate homeostasis in mRNA. It is assumed that m(6)A is mainly demethylated by the -ketoglutarate dependent oxidase ALKBH5. Here we show that ALKBH5 also demethylates the dimethylated adenosine m(2)(6)A, which is a non-canonical base present in ribosomal RNA