Linear versus quadratic detrending in analyzing simultaneous changes in DC-EEG and transcutaneous pCO2. - In: 2023 45th Annual International Conference of the IEEE Engineering in Medicine & Biology Conference (EMBC), (2023), insges. 4 S.
Physiological direct current (DC) potential shifts in electroencephalography (EEG) can be masked by artifacts such as slow electrode drifts. To reduce the influence of these artifacts, linear detrending has been proposed as a pre-processing step. We considered quadratic detrending, which has hardly been addressed for ultralow frequency components in EEG. We compared the performance of linear and quadratic detrending in simultaneously acquired DC-EEG and transcutaneous partial pressure of carbon dioxide during two activation methods: hyperventilation (HV) and apnea (AP). Quadratic detrending performed significantly better than linear detrending in HV, while for AP, our analysis was inconclusive with no statistical significance. We conclude that quadratic detrending should be considered for DC-EEG preprocessing.
https://doi.org/10.1109/EMBC40787.2023.10340855
Why are different estimates of the effective reproductive number so different? : a case study on COVID-19 in Germany. - In: PLoS Computational Biology, ISSN 1553-7358, Bd. 19 (2023), 11, e1011653, S. 1-27
The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.
https://doi.org/10.1371/journal.pcbi.1011653
Analysis of the influence of magnetic blowing field alignments on the DC switching arc :
Analyse des Einflusses magnetischer Blasfeldanordnungen auf den DC-Schaltlichtbogen. - In: Kontaktverhalten und Schalten, (2023), S. 51-60
Collaborative nowcasting of COVID-19 hospitalization incidences in Germany. - In: PLoS Computational Biology, ISSN 1553-7358, Bd. 19 (2023), 8, e1011394, S. 1-25
Real-time surveillance is a crucial element in the response to infectious disease outbreaks. However, the interpretation of incidence data is often hampered by delays occurring at various stages of data gathering and reporting. As a result, recent values are biased downward, which obscures current trends. Statistical nowcasting techniques can be employed to correct these biases, allowing for accurate characterization of recent developments and thus enhancing situational awareness. In this paper, we present a preregistered real-time assessment of eight nowcasting approaches, applied by independent research teams to German 7-day hospitalization incidences during the COVID-19 pandemic. This indicator played an important role in the management of the outbreak in Germany and was linked to levels of non-pharmaceutical interventions via certain thresholds. Due to its definition, in which hospitalization counts are aggregated by the date of case report rather than admission, German hospitalization incidences are particularly affected by delays and can take several weeks or months to fully stabilize. For this study, all methods were applied from 22 November 2021 to 29 April 2022, with probabilistic nowcasts produced each day for the current and 28 preceding days. Nowcasts at the national, state, and age-group levels were collected in the form of quantiles in a public repository and displayed in a dashboard. Moreover, a mean and a median ensemble nowcast were generated. We find that overall, the compared methods were able to remove a large part of the biases introduced by delays. Most participating teams underestimated the importance of very long delays, though, resulting in nowcasts with a slight downward bias. The accompanying prediction intervals were also too narrow for almost all methods. Averaged over all nowcast horizons, the best performance was achieved by a model using case incidences as a covariate and taking into account longer delays than the other approaches. For the most recent days, which are often considered the most relevant in practice, a mean ensemble of the submitted nowcasts performed best. We conclude by providing some lessons learned on the definition of nowcasting targets and practical challenges.
https://doi.org/10.1371/journal.pcbi.1011394
Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations. - In: eLife, ISSN 2050-084X, Bd. 12 (2023), e81916, S. 1-23, insges. 23 S.
https://doi.org/10.7554/eLife.81916
Generalized modeling of photoluminescence transients. - In: Physica status solidi, ISSN 1521-3951, Bd. 260 (2023), 1, 2200339, S. 1-12
Time-resolved photoluminescence (TRPL) measurements and the extraction of meaningful parameters involve four key ingredients: a suitable sample such as a semiconductor double heterostructure, a state-of-the-art measurement setup, a kinetic model appropriate for the description of the sample behavior, and a general analysis method to extract the model parameters of interest from the measured TRPL transients. Until now, the last ingredient is limited to single curve fits, which are mostly based on simple models and least-squares fits. These are often insufficient for the parameter extraction in real-world applications. The goal of this article is to give the community a universal method for the analysis of TRPL measurements, which accounts for the Poisson distribution of photon counting events. The method can be used to fit multiple TRPL transients simultaneously using general kinematic models, but should also be used for single transient fits. To demonstrate this approach, multiple TRPL transients of a GaAs/AlGaAs heterostructure are fitted simultaneously using coupled rate equations. It is shown that the simultaneous fits of several TRPL traces supplemented by systematic error estimations allow for a more meaningful and more robust parameter determination. The statistical methods also quantify the quality of the description by the underlying physical model.
https://doi.org/10.1002/pssb.202200339
Verbund: 05M2018 - KONSENS : Schlussbericht : Förderzeitraum: 01.01.2018-30.06.2021. - Ilmenau : Technische Universität Ilmenau. - 1 Online-Ressource (16 Seiten, 450,82 KB)Förderkennzeichen BMBF 05M18SIA
https://edocs.tib.eu/files/e01fb23/1870887948.pdf
Development of a new antigen-based microarray platform for screening and detection of human IgG antibodies against SARS-CoV-2. - In: Scientific reports, ISSN 2045-2322, Bd. 12 (2022), 8067, S. 1-15
The CoNAN Study Group: Thomas Hotz, Petra Enders, Renate Koch, Steffen Mai, Matthias Ullrich, Cora Richert, Cornelius Eibner, Bettina Meinung, Kay Stötzer, Julia Köhler, Michael Kiehntopf, Hans Cipowicz, Christine Pinkwart, Hans Proquitté, Michael Bauer, Petra Dickmann, Annika Licht, Juliane Scholz, Wibke Wetzker, Anita Hartung, Daniel Weiß, Lara Thieme, Gabi Hanf, Clara Schnizer, Jasmin Müller, Jennifer Kosenkow, Franziska Röstel, Joel Guerra, Oliwia Makarewicz, Steffi Kolanos, Juliane Ankert, Stefan Hagel, Christina Bahrs, Nico Andreas, Raphaela Marquardt, Thomas Kamradt, Sabine Baumgart, Stefanie Deinhardt-Emmer, Sebastian Kuhn, Bettina Löffler, Michael Baier, Stefan Glöckner, André Scherag & Mathias W. Pletz
Strategies to contain the current SARS-CoV-2 pandemic rely, beside vaccinations, also on molecular and serological testing. For any kind of assay development, screening for the optimal antigen is essential. Here we describe the verification of a new protein microarray with different commercially available preparations significant antigens of SARS-CoV-2 that can be used for the evaluation of the performance of these antigens in serological assays and for antibody screening in serum samples. Antigens of other pathogens that are addressed by widely used vaccinations were also included. To evaluate the accuracy of 21 different antigens or antigen preparations on the microarray, receiver operating characteristics (ROC) curve analysis using ELISA results as reference were performed. Except for a single concentration, a diagnostic sensitivity of 1 was determined for all antigen preparations. A diagnostic specificity, as well as an area under the curve (AUC) of 1 was obtained for 16 of 21 antigen preparations. For the remaining five, the diagnostic specificity ranged from 0.942 to 0.981 and AUC from 0.974 to 0.999. The optimized assay was subsequently also applied to determine the immune status of previously tested individuals and/or to detect the immunization status after COVID-19 vaccination. Microarray evaluation of the antibody profiles of COVID-19 convalescent and post vaccination sera showed that the IgG response differed between these groups, and that the choice of the test antigen is crucial for the assay performance. Furthermore, the results showed that the immune response is highly individualized, depended on several factors (e.g., age or sex), and was not directly related to the severity of disease. The new protein microarray provides an ideal method for the parallel screening of many different antigens of vaccine-preventable diseases in a single sample and for reliable and meaningful diagnostic tests, as well as for the development of safe and specific vaccines.
https://doi.org/10.1038/s41598-022-10823-7
Microfluidically-assisted isolation and characterization of Achromobacter spanius from soils for microbial degradation of synthetic polymers and organic solvents. - In: Environments, ISSN 2076-3298, Bd. 9 (2022), 12, 147, S. 1-17
A micro segmented-flow approach was utilized for the isolation soil bacteria that can degrade synthetic polymers as polyethylene glycols (PEG) and polyacrylamide (PAM). We had been able to obtain many strains; among them, five Achromobacter spanius strains from soil samples of specific sampling sites that were connected with ancient human impacts. In addition to the characterization of community responses and isolating single strains, this microfluidic approach allowed for investigation of the susceptibility of Achromobacter spanius strains against three synthetic polymers, including PEG, PAM, and Polyvinylpyrrolidone (PVP) and two organic solvents known as 1,4-dioxane and diglyme. The small stepwise variation of effector concentrations in 500 nL droplets provides a detailed reflection of the concentration-dependent response of bacterial growth and endogenous autofluorescence activity. As a result, all five strains can use PEG600 as carbon source. Furthermore, all strains showed similar dose-response characteristics in 1,4-dioxane and diglyme. However, significantly different PAM- and PVP-tolerances were found for these strains. Samples from the surface soil of prehistorical rampart areas supplied a strain capable of degradation of PEG, PVP, and PAM. This study demonstrates on the one hand, the potential of microsegment flow for miniaturized dose-response screening studies and its ability to detect novel strains, and on the other hand, two of five isolated Achromobacter spanius strains may be useful in providing optimal growth conditions in bioremediation and biodegradation processes.
https://doi.org/10.3390/environments9120147
National and subnational short-term forecasting of COVID-19 in Germany and Poland during early 2021. - In: Communications medicine, ISSN 2730-664X, Bd. 2 (2022), 136, S. 1-17
During the COVID-19 pandemic there has been a strong interest in forecasts of the short-term development of epidemiological indicators to inform decision makers. In this study we evaluate probabilistic real-time predictions of confirmed cases and deaths from COVID-19 in Germany and Poland for the period from January through April 2021.
https://doi.org/10.1038/s43856-022-00191-8
Analysis of safety-critical cloud architectures with multi-trajectory simulation. - In: 2022 Annual Reliability and Maintainability Symposium (RAMS), (2022), insges. 7 S.
Dynamic safety-critical systems require model-based techniques and tools for their systems design. The paper presents a stochastic Petri net model of an industrial safetycritical cloud server architecture for train control. Its reliability has to be evaluated to assess tradeoffs in architecture and level of fault tolerance. Simulation methods are too slow for such rare-event problems, while numerical analysis techniques suffer from the state-space explosion problem. The paper extends a recently developed multi-trajectory simulation algorithm combining elements of simulation and numerical analysis such that it increases the accuracy of rare-event simulations within a given computation time budget. Simulation experiments have been carried out with a prototype tool.
https://doi.org/10.1109/RAMS51457.2022.9893923
How much testing and social distancing is required to control COVID-19? : some insight based on an age-differentiated compartmental model. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 60 (2022), 2, S. S145-S169
In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: incubation time, age-dependent symptom severity, and testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.
https://doi.org/10.1137/20M1377783
A pre-registered short-term forecasting study of COVID-19 in Germany and Poland during the second wave. - In: Nature Communications, ISSN 2041-1723, Bd. 12 (2021), 5173, S. 1-16
Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October-19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.
https://doi.org/10.1038/s41467-021-25207-0
How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks. - In: SIAM journal on applied dynamical systems, ISSN 1536-0040, Bd. 20 (2021), 2, S. 1135-1157
Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision-making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the health care system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.
https://doi.org/10.1137/20M1387687
Admissible kernels for RKHS embedding of probability distributions. - In: Statistical papers, ISSN 1613-9798, Bd. 62 (2021), 3, S. 1499-1518
Similarity measurement of two probability distributions is important in many applications of statistics. Embedding such distributions into a reproducing kernel Hilbert space (RKHS) has many favorable properties. The choice of the reproducing kernel is crucial in the approach. We study this question by considering the similarity of two distributions of the same class. In particular, we investigate when the RKHS embedding is "admissible" in the sense that the distance between the embeddings should become smaller when the expectations are getting closer or when the variance is increasing to infinity. We give conditions on the widely-used translation-invariant reproducing kernels to be admissible. We also extend the study to multivariate non-symmetric Gaussian distributions.
https://doi.org/10.1007/s00362-019-01144-5
Integrating simulation and numerical analysis in the evaluation of generalized stochastic Petri nets. - In: ACM transactions on modeling and computer simulation, ISSN 1558-1195, Bd. 29 (2019), 4, S. 24:1-24:25
https://dx.doi.org/10.1145/3321518
Packing bounds for outer products with applications to compressive sensing. - In: Geometric science of information, (2019), S. 135-143
An algorithm for computing Fréchet means on the sphere. - In: Optimization letters, ISSN 1862-4480, Bd. 13 (2019), 7, S. 1523-1533
For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special global problem over the sphere, namely the determination of Fréchet means, which are points minimising the mean distance to a given set of points. The Branch and Bound method derived needs no further assumptions on the input data, but is able to cope with this objective function which is neither convex nor differentiable. The algorithms performance is tested on simulated and real data.
https://doi.org/10.1007/s11590-019-01415-y
Grid-free Direction-of-Arrival estimation with compressed sensing and arbitrary antenna arrays. - In: 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ISBN 978-1-5386-4658-8, (2018), S. 3251-3255
https://doi.org/10.1109/ICASSP.2018.8462501
Sparsity order estimation from a single compressed observation vector. - In: IEEE transactions on signal processing, ISSN 1941-0476, Bd. 66 (2018), 15, S. 3958-3971
https://doi.org/10.1109/TSP.2018.2841867
Towards energy consumption prediction with safety margins for multicopter systems. - In: Proceedings of the 11th EAI International Conference on Performance Evaluation Methodologies and Tools, ISBN 978-1-4503-6346-4, (2017), S. 227-228
Fast abstract
https://doi.org/10.1145/3150928.3150964
Constructing universal, non-asymptotic confidence sets for intrinsic means on the circle. - In: Geometric Science of Information, (2017), S. 477-485
https://doi.org/10.1007/978-3-319-68445-1_56
A hybrid multi-trajectory simulation algorithm for the performance evaluation of stochastic petri nets. - In: Quantitative Evaluation of Systems, (2017), S. 107-122
https://doi.org/10.1007/978-3-319-66335-7_7
Projective shapes : topology and means. - Ilmenau : Universitätsbibliothek, 2017. - 1 Online-Ressource (82 Seiten)
Technische Universität Ilmenau, Dissertation 2017
Die projektive Form eines Objektes ist die geometrische Information, die invariant unter projektiven Transformationen ist. Sie tritt natürlicherweise bei der Rekonstruktion von Objekten anhand Fotos unkalibrierter Kameras auf. Wenn ein Objekt als Punktmenge oder Konfiguration von Landmarken im d-dimensionalen reell-projektiven Raum RP(d) beschrieben wird, so ist die Menge der projektiven Formen der Quotientenraum RP(d)^k / PGL(d) und damit kanonisch mit der Quotiententopologie versehen. Auf diesem topologischen Raum der projektiven Formen lassen sich jedoch aus topologischen Gründen viele mathematische Werkzeuge nicht anwenden, ein Phänomen, welches in ähnlicher Form auch bei den Räumen der Ähnlichkeits- bzw. affinen Formen auftritt. In der vorliegenden Arbeit wird die Topologie des projektiven Formenraumes gründlich untersucht, in Hinblick auf die Suche nach einem vernünftigen topologischen Unterraum, der hinreichende Eigenschaften für die Anwendung statistischer Methoden besitzt. Ein Beispiel für einen dieser gutartigen Unterräume ist der Raum der Tyler regulären Formen, der bereits durch Kent und Mardia betrachtet wurde. Deren Ergebnisse werden in dieser Arbeit noch erweitert. Dieser Unterraum ist zwar für einige Dimensionen d und Anzahlen an Landmarken k nicht optimal gewählt, jedoch liefert die sogenannte Tyler-Standardisierung dieser Formen einem sowohl Einbettungen in metrische Räume als auch eine Riemannsche Metrik auf diesem Unterraum. Für eine dieser Einbettungen werden die dazugehörige Fréchet-Erwartungs- sowie Mittelwerte definiert. Während die Konsistenz dieses Mittelwertes leicht zu zeigen ist, ist die Berechnung des extrinsischen Mittelwertes numerisch anspruchsvoll. Als Ersatz wird ein weiterer Erwartungs- bzw. Mittelwert definiert, dessen Berechnung diese Probleme umgeht.
http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2017000404
Asymmetry parameter of peaked Fano line shapes. - In: Review of scientific instruments, ISSN 1089-7623, Bd. 87 (2016), 10, S. 103901, insges. 7 S.
The spectroscopic line shape of electronic and vibrational excitations is ubiquitously described by a Fano profile. In the case of nearly symmetric and peaked Fano line shapes, the fit of the conventional Fano function to experimental data leads to difficulties in unambiguously extracting the asymmetry parameter, which may vary over orders of magnitude without degrading the quality of the fit. Moreover, the extracted asymmetry parameter depends on initially guessed values. Using the spectroscopic signature of the single-Co Kondo effect on Au(110) the ambiguity of the extracted asymmetry parameter is traced to the highly symmetric resonance profile combined with the inevitable scattering of experimental data. An improved parameterization of the conventional Fano function is suggested that enables the nonlinear optimization in a reduced parameter space. In addition, the presence of a global minimum in the sum of squared residuals and thus the independence of start parameters may conveniently be identified in a two-dimensional plot. An angular representation of the asymmetry parameter is suggested in order to reliably determine uncertainty margins via linear error propagation.
http://dx.doi.org/10.1063/1.4963678
Non-asymptotic confidence sets for circular means. - In: Entropy, ISSN 1099-4300, Bd. 18 (2016), 10, 375, S. 1-13
https://doi.org/10.3390/e18100375
Universal, non-asymptotic confidence sets for circular means. - In: Geometric Science of Information, (2015), S. 635-642
http://dx.doi.org/10.1007/978-3-319-25040-3_68
Intrinsic means on the circle: uniqueness, locus and asymptotics. - In: Annals of the Institute of Statistical Mathematics, ISSN 1572-9052, Bd. 67 (2015), 1, S. 177-193
http://dx.doi.org/10.1007/s10463-013-0444-7
Sparsity order estimation for single snapshot compressed sensing. - In: 48th Asilomar Conference on Signals, Systems and Computers, 2014, ISBN 978-1-4799-8298-1, (2014), S. 1220-1224
http://dx.doi.org/10.1109/ACSSC.2014.7094653
Random approximations in multiobjective optimization. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2014. - Online-Ressource (PDF-Datei: 27 S., 304,7 KB). - (Preprint ; M14,12)
Often decision makers have to cope with a programming problem with unknown quantitities. Then they will estimate these quantities and solve the problem as it then appears - the 'approximate problem'. Thus there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. Confidence sets, i.e. sets that cover the true sets with a given prescribed probability, provide useful quantitative information. In this paper we consider multiobjective problems and derive confidence sets for the sets of efficient points, weakly efficient points, and the corresponding solution sets. Besides the crucial convergence conditions for the objective and/or constraint functions, one approach for the derivation of confidence sets requires some knowledge about the true problem, which may be not available. Therefore also another method, called relaxation, is suggested. This approach works without any knowledge about the true problem. The results are applied to the Markowitz model of portfolio optimization.
http://www.db-thueringen.de/servlets/DocumentServlet?id=25361
Multiscale DNA partitioning: statistical evidence for segments. - In: Bioinformatics, ISSN 1367-4811, Bd. 30 (2014), 16, S. 2255-2262
http://dx.doi.org/10.1093/bioinformatics/btu180
On means and their asymptotics: circles and shape spaces. - In: Journal of mathematical imaging and vision, ISSN 1573-7683, Bd. 50 (2014), 1/2, S. 98-106
https://doi.org/10.1007/s10851-013-0462-3
Idealizing ion channel recordings by a jump segmentation multiresolution filter. - In: IEEE transactions on nanobioscience, ISSN 1558-2639, Bd. 12 (2013), 4, S. 376-386
http://dx.doi.org/10.1109/TNB.2013.2284063
Sticky central limit theorems on open books. - In: The annals of applied probability, ISSN 2168-8737, Bd. 23 (2013), 6, S. 2238-2258
http://projecteuclid.org/euclid.aoap/1382447687
Extrinsic vs intrinsic means on the circle. - In: Geometric Science of Information, (2013), S. 433-440
http://dx.doi.org/10.1007/978-3-642-40020-9_47
A uniform concentration-of-measure inequality for multivariate kernel density estimators. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2013. - Online-Ressource (PDF-Datei: 10 S., 264,6 KB). - (Preprint ; M13,09)
Confidence sets for modes or level sets of densities are usually derived from the asymptotic distribution of a suitable statistic. Mostly one does not have further information about how close the asymptotic distribution comes to the true distribution for a fixed sample size n. In order to derive conservative cofindence sets for each sample size recently an approach was suggested that does not need full information about a distribution, but instead employs a quantified version of semi-convergence in probability of random sets. The application of this approach to modes or level sets of density functions requires uniform concentration-of-measure results for the density estimators. The aim of the present paper is to prove a result of that kind for the multivariate kernel density estimator. The inequality is also of own interest as it provides a conservative confidence band for the density function.
http://www.db-thueringen.de/servlets/DocumentServlet?id=22415
Universal confidence sets for the mode of a regression function. - In: IMA journal of management mathematics, ISSN 1471-6798, Bd. 23 (2012), 4, S. 309-323
http://dx.doi.org/10.1093/imaman/dps011
What is special about patients with lung cancer and pulmonary metastases in palliative care? : results from a nationwide survey. - In: Journal of palliative medicine, ISSN 1557-7740, Bd. 15 (2012), 9, S. 971-977
http://dx.doi.org/10.1089/jpm.2011.0434
Universal confidence sets - estimation and relaxation. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2011. - Online-Ressource (PDF-Datei: 14 S., 192,5 KB). - (Preprint ; M11,12)
http://www.db-thueringen.de/servlets/DocumentServlet?id=18490
Universal confidence sets for the mode of a regression function. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2010. - Online-Ressource (PDF-Datei: 17 S., 211 KB). - (Preprint ; M10,02)
http://www.db-thueringen.de/servlets/DocumentServlet?id=14876
On optimal estimation of a non-smooth mode in a nonparametric regression model with [alpha]-mixing errors. - In: Journal of statistical planning and inference, ISSN 0378-3758, Bd. 140 (2010), 2, S. 406-418
http://dx.doi.org/10.1016/j.jspi.2009.07.016
Condidence sets and convergence of random functions. - In: Festschrift in celebration of Prof. Dr. Wilfried Grecksch's 60th birthday, (2008), S. 227-245
Universal confidence sets for solutions of optimization problems. - In: SIAM journal on optimization, ISSN 1095-7189, Bd. 19 (2008), 3, S. 1467-1488
https://doi.org/10.1137/070680023
Universal confidence sets - sufficient conditions. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2008. - 15 S. = 192,5 KB, Text. - (Preprint ; M08,06)
http://www.db-thueringen.de/servlets/DocumentServlet?id=10380
Convergence in distribution of random closed sets and applications in stability theory of stochastic optimisation, 2007. - Online-Ressource (PDF-Datei: 159 S., 674 KB) : Ilmenau, Techn. Univ., Diss., 2007
Parallel als Druckausg. erschienen
In dieser Dissertation wird die einseitige Konvergenz in Verteilung fuer abgeschlossene zufaellige Mengen und deren Anwendung auf stochastische Optimierungsprobleme untersucht. Ausgehend von den Konvergenzbegriffen von Kuratowski-Painleve wird Konvergenz in Verteilung basierend auf Hit- und Miss- Topologien definiert. Wichtige Hilfsmittel wie das Continuous Mapping Theorem und halbstetige Verallgemeinerungen werden bereitgestellt. Es wird eine Vielzahl von hinreichenden Bedingungen fuer die Konvergenz der Epigraphen zufaelliger unterhalbstetiger Funktionen bewiesen. Dabei wird gezeigt, wie Klassen stochastischer Prozesse dem Mengenkonvergenzansatz zugaenglich gemacht werden koennen. Neben der unterhalbstetigen Modifikation der Skorohod-Raeume D wird mit Hilfe der Methode der Konvergenz endlichdimensionaler Verteilungen ein neues Konvergenzkriterium fuer die Konvergenz stochastischer Prozesse mit unterhalbstetigen Trajektorien bewiesen. Aussagen ueber die Konvergenz in Verteilung der optimalen Werte und der Loesungsmengen stochastischer Optimierungsprobleme werden hergeleitet und fuer einseitige Abschaetzungen und Konfidenzbereiche angewendet. Im letzen Kapitel wird gezeigt, wie sich das Konzept der einseitigen Mengenkonvergenz in Verteilung auf die Menge der effizienten Punkte und die Loesungsmengen stochastischer Vektoroptimierungsprobleme anwenden laesst. Hierbei wird wie in der eindimensionalen Optimierung auch die naeherungsweise Optimalitaet (epsilon optimality) betrachtet.
http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2007000011
Universal confidence sets for solutions of optimization problems. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2006. - 25 S. = 288,1 KB. - (Preprint ; M06,12)
http://www.db-thueringen.de/servlets/DocumentServlet?id=7411
Semiconvergence in distribution of random closed sets with application to random optimization problems. - In: Annals of operations research, ISSN 1572-9338, Bd. 142 (2006), 1, S. 269-282
http://dx.doi.org/10.1007/s10479-006-6172-0
Strong convergence of estimators as [epsilon]n-minimisers of optimisation problems. - In: Annals of the Institute of Statistical Mathematics, ISSN 1572-9052, Bd. 57 (2005), 2, S. 291-313
http://dx.doi.org/10.1007/BF02507027
Qualitative stability of stochastic programs with applications in asymptotic statistics. - In: Statistics & decisions, ISSN 0721-2631, Bd. 23 (2005), 3, S. 219-248
On stability of multistage stochastic decision problems. - In: Recent advances in optimization, (2005), S. 103-118
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