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Zimmermann, Armin; Hotz, Thomas;
Integrating simulation and numerical analysis in the evaluation of generalized stochastic Petri nets. - In: ACM transactions on modeling and computer simulation : TOMACS.. - New York, NY : ACM Press, ISSN 1558-1195, Bd. 29 (2019), 4, S. 24:1-24:25

https://dx.doi.org/10.1145/3321518
Semper, Sebastian; Hotz, Thomas;
Packing bounds for outer products with applications to compressive sensing. - In: Geometric science of information. - Cham : Springer, (2019), S. 135-143

Eichfelder, Gabriele; Hotz, Thomas; Wieditz, Johannes;
An algorithm for computing Fréchet means on the sphere. - In: Optimization letters. - Berlin : Springer, 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
Semper, Sebastian; Römer, Florian; Hotz, Thomas; Del Galdo, Giovanni;
Grid-free Direction-of-Arrival estimation with compressed sensing and arbitrary antenna arrays. - In: 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing : proceedings : April 15-20, 2018, Calgary Telus Convention Center, Calgary, Alberta, Canada.. - Piscataway, NJ : IEEE, ISBN 978-1-5386-4658-8, (2018), S. 3251-3255

https://doi.org/10.1109/ICASSP.2018.8462501
Semper, Sebastian; Römer, Florian; Hotz, Thomas; Del Galdo, Giovanni;
Sparsity order estimation from a single compressed observation vector. - In: IEEE transactions on signal processing : SP ; a publication of the IEEE Signal Processing Society.. - New York, NY : IEEE, Bd. 66 (2018), 15, S. 3958-3971

https://doi.org/10.1109/TSP.2018.2841867
Hotz, Thomas;
Hilft Honig Husten heilen?. - In: Kinderuni Ilmenau 2017. - Ilmenau, (2017)

Dietrich, Thomas; Krug, Silvia; Hotz, Thomas; Zimmermann, Armin;
Towards energy consumption prediction with safety margins for multicopter systems. - In: Proceedings of the 11th EAI International Conference on Performance Evaluation Methodologies and Tools : VALUETOOLS 2017 : 5-7 December 2017, Venice, Italy.. - New York, NY, USA : ACM, ISBN 978-1-4503-6346-4, (2017), S. 227-228
- Fast abstract

https://doi.org/10.1145/3150928.3150964
Glock, Matthias; Hotz, Thomas;
Constructing universal, non-asymptotic confidence sets for intrinsic means on the circle. - In: Geometric science of information : third International Conference, GSI 2017, Paris, France, November 7-9, 2017 : proceedings.. - Cham : Springer International Publishing, ISBN 978-3-319-68445-1, (2017), S. 477-485

https://doi.org/10.1007/978-3-319-68445-1_56
Zimmermann, Armin; Hotz, Thomas; Canabal Lavista, Andrés;
A hybrid multi-trajectory simulation algorithm for the performance evaluation of stochastic petri nets. - In: Quantitative Evaluation of Systems : 14th International Conference, QEST 2017, Berlin, Germany, September 5-7, 2017, Proceedings.. - Cham : Springer, (2017), S. 107-122

https://doi.org/10.1007/978-3-319-66335-7_7
Vogel, Silvia;
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
Vogel, Silvia; Schettler, Anne
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)
http://www.db-thueringen.de/servlets/DocumentServlet?id=22415
Sinotina, Tatiana; Vogel, Silvia
Universal confidence sets for the mode of a regression function. - In: IMA journal of management mathematics. - Oxford : Univ. Press, ISSN 1471-6798, Bd. 23 (2012), 4, S. 309-323

http://dx.doi.org/10.1093/imaman/dps011
Vogel, Silvia;
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
Sinotina, Tatiana; Vogel, Silvia
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
Wieczorek, Barbara; Ziegler, Klaus
On optimal estimation of a non-smooth mode in a nonparametric regression model with [alpha]-mixing errors. - In: Journal of statistical planning and inference : JSPI.. - Amsterdam : North-Holland Publ. Co., ISSN 0378-3758, Bd. 140 (2010), 2, S. 406-418

http://dx.doi.org/10.1016/j.jspi.2009.07.016
Vogel, Silvia;
Condidence sets and convergence of random functions. - In: Festschrift in celebration of Prof. Dr. Wilfried Grecksch's 60th birthday. - Aachen : Shaker, ISBN 978-3-8322-7500-6, (2008), S. 227-245

Vogel, Silvia;
Universal confidence sets for solutions of optimization problems. - In: SIAM journal on optimization. - Philadelphia, Pa. : SIAM, ISSN 1095-7189, Bd. 19 (2008), 3, S. 1467-1488

https://doi.org/10.1137/070680023
Vogel, Silvia;
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
Gersch, Oliver;
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

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
Vogel, Silvia;
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
Vogel, Silvia;
Semiconvergence in distribution of random closed sets with application to random optimization problems. - In: Annals of operations research. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1572-9338, Bd. 142 (2006), 1, S. 269-282

http://dx.doi.org/10.1007/s10479-006-6172-0
Lachout, Petr; Liebscher, Eckhard; Vogel, Silvia
Strong convergence of estimators as [epsilon]n-minimisers of optimisation problems. - In: Annals of the Institute of Statistical Mathematics. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1572-9052, Bd. 57 (2005), 2, S. 291-313

http://dx.doi.org/10.1007/BF02507027
Vogel, Silvia;
Qualitative stability of stochastic programs with applications in asymptotic statistics. - In: Statistics & decisions. - München : Oldenbourg, ISSN 0721-2631, Bd. 23 (2005), 3, S. 219-248

Mänz, Alexander; Vogel, Silvia
On stability of multistage stochastic decision problems. - In: Recent advances in optimization. - Berlin [u.a.] : Springer, ISBN 978-3-540-28257-0, (2005), S. 103-118

Ziegler, Klaus;
Adaptive kernel estimation of the mode in a nonparametric design regression model. - In: Probability and mathematical statistics. - Wrocław : Wydawn. Uniw. Wrocławskiego, ISSN 0208-4147, Bd. 24 (2004), 2, S. 213-235

Herrmann, Eva; Ziegler, Klaus
Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions. - In: Statistics & probability letters. - Amsterdam : Elsevier Science, Bd. 68 (2004), 4, S. 359-368

http://dx.doi.org/10.1016/j.spl.2004.04.005
Vogel, Silvia;
Stochastic programming and statistical estimates. - In: Operations research proceedings 2003. - Berlin [u.a.] : Springer, (2004), S. 443-450
- Literaturangaben

Liebscher, Eckhard;
Strong convergence of estimators in nonlinear autoregressive models. - In: Journal of multivariate analysis : JMVA.. - Orlando, Fla. : Acad. Press, Bd. 84 (2003), 2, S. 247-261

http://dx.doi.org/10.1016/S0047-259X(02)00022-2
Herrmann, Eva; Ziegler, Klaus
Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2003. - 11 S. = 151,1 KB. . - (Preprint. - M03,14)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5727
Ziegler, Klaus;
On kernel estimation of curves with non-smooth peaks. - Ilmenau : Techn. Univ., Inst. für Mathematik, 2003. - 12 S. = 140,6 KB. . - (Preprint. - M03,13)
http://www.db-thueringen.de/servlets/DocumentServlet?id=5726
Ziegler, Klaus;
On the asymptotic normality of kernel regression estimators of the mode in the nonparametric random design model. - In: Journal of statistical planning and inference : JSPI.. - Amsterdam : North-Holland Publ. Co., ISSN 0378-3758, Bd. 115 (2003), 1, S. 123-144

http://dx.doi.org/10.1016/S0378-3758(02)00152-0
Lachout, Petr; Vogel, Silvia
On continuous convergence and epi-convergence of random functions : sufficent conditions and applications (part II). - In: Kybernetika. - Praha, ISSN 0023-5954, Bd. 39 (2003), 1, S. 99-118

Lachout, Petr; Vogel, Silvia
On continuous convergence and epi-convergence of random functions : theory and relations (part I). - In: Kybernetika. - Praha, ISSN 0023-5954, Bd. 39 (2003), 1, S. 75-98

Liebscher, Eckhard;
Kernel density and hazard rate estimation for censored data under [alpha]-mixing condition. - In: Annals of the Institute of Statistical Mathematics. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1572-9052, Bd. 54 (2002), 1, S. 19-28

http://dx.doi.org/10.1023/A:1016157519826
Vogel, Silvia;
Approximation von stochastischen Optimierungsproblemen. - In: Haupt- und Kurzvorträge der 4. Tagung der deutschen Sektion am 9. und 10. Oktober 2000 an der Technischen Universität Chemnitz, Fakultät für Mathematik. - Chemnitz : Techn. Univ., Fak. für Mathematik, (2001), S. 39-46

Liebscher, Eckhard;
Central limit theorems for a-mixing triangular arrays with applications to nonparametric statistics. - In: Mathematical methods of statistics. - New York, NY : Allerton Press, ISSN 1066-5307, Bd. 10 (2001), 2, S. 194-214

Liebscher, Eckhard;
Estimation of the density and the regression function under mixing conditions. - In: Statistics & decisions. - München : Oldenbourg, ISSN 0721-2631, Bd. 19 (2001), 1, S. 9-26

Liebscher, Eckhard;
Estimating the density of the residuals in autoregressive models. - In: Statistical inference for stochastic processes. - Dordrecht [u.a.] : Springer Science + Business Media B.V, ISSN 1572-9311, Bd. 2 (1999), 2, S. 105-117

http://dx.doi.org/10.1023/A:1009924821271
Liebscher, Eckhard;
Asymptotic normality of nonparametric estimators under α-mixing condition. - In: Statistics & probability letters. - Amsterdam : Elsevier Science, Bd. 43 (1999), 3, S. 243-250

http://dx.doi.org/10.1016/S0167-7152(98)00264-8
Vogel, Silvia;
Random approximations in multiobjective programming with an application to portfolio optimization with shortfall constraints. - In: Control and cybernetics. - Warszawa : SRI PAS, ISSN 0324-8569, Bd. 28 (1999), 4, S. 703-724

Fabricius, Alexander; Breternitz, Volkmar; Knedlik, Christian; Henning, Andreas; Liebscher, Eckhard; Vogel, Silvia
Investigations of electromigration failure by electrical measurement and scanning probe microscopy with additional simulation. - In: Materials reliability in microelectronics VIII. - Warrendale, Pa. : Materials Research Soc., (1998), S. 27-32

Liebscher, Eckhard;
On a class of plug-in methods of bandwidth selection for kernel density estimators. - In: Statistics & decisions. - München : Oldenbourg, ISSN 0721-2631, Bd. 16 (1998), S. 229-243

Liebscher, Eckhard;
Convergence of hermite series density estimators under conditions of weak dependence. - In: Statistics. - Abingdon, Oxon [u.a.] : Taylor & Francis, ISSN 0233-1888, Bd. 31 (1998), 3, S. 191-214

Henning, Andreas; Liebscher, Eckhard; Vogel, Silvia; Fabricius, Alexander; Breternitz, Volkmar; Knedlik, Christian
Simulation des Ausfallverhaltens von Al (Si Cu) Leitbahnen mit Hilfe von Threshold-Modellen. - In: 43. Internationales Wissenschaftliches Kolloquium. - Ilmenau: Tech. Univ., (1998), insges. 6 S.

Liebscher, Eckhard; Schäbe, Hendrik
A generalization of the Kaplan-Meier estimator to Harris-recurrent Markov chains. - In: Statistical papers. - Berlin : Springer, ISSN 1613-9798, Bd. 38 (1997), 1, S. 63-75

http://dx.doi.org/10.1007/BF02925215
Heinrich, Lothar; Liebscher, Eckhard
Strong convergence of kernel estimators for product densities of absolutely regular point processes. - In: Journal of nonparametric statistics. - Abingdon : Taylor & Francis, ISSN 1048-5252, Bd. 8 (1997), 1, S. 65-96

Henning, Andreas;
Nichtlineare autoregressive Modelle der Zeitreihenanalyse. - In: Beiträge aus dem wissenschaftlichen Leben. - Ilmenau : Univ., Bd. 2 (1997), S. 18-21

Liebscher, Eckhard;
Strong convergence of sums of α-mixing random variables with applications to density estimation. - In: Stochastic processes and their applications. - Amsterdam [u.a.] : Elsevier, Bd. 65 (1996), 1, S. 69-80

http://dx.doi.org/10.1016/S0304-4149(96)00096-8
Liebscher, Eckhard;
Central limit theorems for sums of a-mixing random variables. - In: Stochastics and stochastics reports. - Abingdon : Taylor & Francis, ISSN 1045-1129, Bd. 59 (1996), 3/4, S. 241-258

Liebscher, Eckhard;
Strong convergence of sums of [phi]-mixing random variables. - In: Mathematical methods of statistics. - New York, NY : Allerton Press, ISSN 1066-5307, Bd. 4 (1995), 2, S. 216-229

Vogel, Silvia;
A stochastic approach to stability in stochastic programming. - In: Journal of computational and applied mathematics. - Amsterdam [u.a.] : North-Holland, Bd. 56 (1994), 1/2, S. 65-96

https://doi.org/10.1016/0377-0427(94)90380-8
Liebscher, Eckhard;
Beiträge zur nichtparametrischen Statistik. - 204 Bl. Ilmenau : Techn. Univ., Habil.-Schr., 1994