TY - CHAP A1 - Bozakov, Zdravko A1 - Sander, Volker T1 - OpenFlow: A Perspective for Building Versatile Networks T2 - Network-Embedded Management and Applications Y1 - 2013 SN - 978-1-4419-6769-5 U6 - http://dx.doi.org/10.1007/978-1-4419-6769-5_11 SP - 217 EP - 245 PB - Springer CY - New York, NY ER - TY - JOUR A1 - Huck, Christina A1 - Jolly, Christina A1 - Wagner, Patrick A1 - Poghossian, Arshak A1 - Schöning, Michael Josef T1 - One-chip integrated dual amperometric/field-effect sensor for the detection of dissolved hydrogen JF - Procedia Engineering. 25 (2011) Y1 - 2011 SN - 1877-7058 N1 - EurosensorsXXV ; Proc. Eurosensors XXV, September 4-7, 2011, Athens, Greece SP - 1161 EP - 1164 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Müller-Veggian, Mattea A1 - Beuscher, H. A1 - Haenni, D. R. A1 - Gono, Y. T1 - On-line experiments with the orange-β-spectrometer JF - Annual report 1977 / Institut für Kernphysik Kernforschungsanlage Jülich Y1 - 1978 N1 - Spezielle Berichte der Kernforschungsanlage Jülich ; 15 SP - 51 EP - 52 PB - Verlag des Forschungszentrums Jülich CY - Jülich ER - TY - JOUR A1 - Pieronek, Lukas A1 - Kleefeld, Andreas T1 - On trajectories of complex-valued interior transmission eigenvalues JF - Inverse problems and imaging : IPI N2 - This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection. KW - Interior transmission problem KW - Eigenvalue trajectories KW - Complex-valued eigenvalues Y1 - 2024 U6 - http://dx.doi.org/10.3934/ipi.2023041 SN - 1930-8337 (Print) SN - 1930-8345 (Online) VL - 18 IS - 2 SP - 480 EP - 516 PB - AIMS CY - Springfield, Mo ER - TY - JOUR A1 - Reißel, Martin A1 - Quell, P. T1 - On the Vanishing Displacement Current Limit for Eddy-Current Problems / Quell, P. ; Reißel, M. JF - ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik. 76 (1996), H. S2 Y1 - 1996 SN - 0044-2267 N1 - ICIAM/GAMM 95 Applied Analysis SP - 649 EP - 650 ER - TY - JOUR A1 - Stulpe, Werner T1 - On the Representation of Quantum Mechanics on Phase Space JF - International Journal of Theoretical Physics. 31 (1992), H. 9 Y1 - 1992 SN - 1572-9575 SP - 1785 EP - 1795 ER - TY - JOUR A1 - Stulpe, Werner T1 - On the Representation of Quantum Mechanics on a Classical Sample Space JF - International Journal of Theoretical Physics. 37 (1998), H. 1 Y1 - 1998 SN - 1572-9575 SP - 349 EP - 356 ER - TY - JOUR A1 - Gaigall, Daniel T1 - On the applicability of several tests to models with not identically distributed random effects JF - Statistics : A Journal of Theoretical and Applied Statistics N2 - We consider Kolmogorov–Smirnov and Cramér–von-Mises type tests for testing central symmetry, exchangeability, and independence. In the standard case, the tests are intended for the application to independent and identically distributed data with unknown distribution. The tests are available for multivariate data and bootstrap procedures are suitable to obtain critical values. We discuss the applicability of the tests to random effects models, where the random effects are independent but not necessarily identically distributed and with possibly unknown distributions. Theoretical results show the adequacy of the tests in this situation. The quality of the tests in models with random effects is investigated by simulations. Empirical results obtained confirm the theoretical findings. A real data example illustrates the application. KW - central symmetry test KW - exchangeability test KW - independence test KW - random effects KW - not identically distributed Y1 - 2023 SN - 0323-3944 U6 - http://dx.doi.org/10.1080/02331888.2023.2193748 SN - 1029-4910 VL - 57 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Grotendorst, Johannes A1 - Jansen, Paul A1 - Schoberth, Siegfried T1 - On Solving the McConnell Equations in Biochemistry / Grotendorst, Johannes ; Jansen, Paul ; Schoberth, Siegfried JF - MapleTech. 1 (1993) Y1 - 1993 SN - 1061-5733 N1 - zgl. Technical Report KFA-ZAM-IB-9314 ; The Maple Technical Newsletter SP - 56 EP - 62 ER - TY - JOUR A1 - Dikta, Gerhard T1 - On Semiparametric Random Censorship Models JF - Journal of Statistical Planning and Inference. 66 (1998), H. 2 Y1 - 1998 SN - 0378-3758 SP - 253 EP - 279 ER - TY - THES A1 - Gaigall, Daniel T1 - On selected problems in multivariate analysis N2 - Selected problems in the field of multivariate statistical analysis are treated. Thereby, one focus is on the paired sample case. Among other things, statistical testing problems of marginal homogeneity are under consideration. In detail, properties of Hotelling‘s T² test in a special parametric situation are obtained. Moreover, the nonparametric problem of marginal homogeneity is discussed on the basis of possibly incomplete data. In the bivariate data case, properties of the Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic on the basis of partly not identically distributed data are investigated. Similar testing problems are treated within the scope of the application of a result for the empirical process of the concomitants for partly categorial data. Furthermore, testing changes in the modeled solvency capital requirement of an insurance company by means of a paired sample from an internal risk model is discussed. Beyond the paired sample case, a new asymptotic relative efficiency concept based on the expected volumes of multidimensional confidence regions is introduced. Besides, a new approach for the treatment of the multi-sample goodness-of-fit problem is presented. Finally, a consistent test for the treatment of the goodness-of-fit problem is developed for the background of huge or infinite dimensional data. KW - Paired sample KW - Marginal homogeneity KW - Incomplete data KW - Asymptotic relative efficiency KW - Volumes of confidence regions Y1 - 2023 U6 - http://dx.doi.org/10.15488/14304 N1 - Gottfried Wilhelm Leibniz Universität Hannover ER - TY - JOUR A1 - Reißel, Martin A1 - Herbst, Michael A1 - Gottschalk, Swen A1 - Hardelauf, Horst T1 - On preconditioning for a parallel solution of the Richards equation / Herbst, Michael ; Gottschalk, Swen ; Reißel, Martin ; Hardelauf, Horst ; Kasteel, Roy ; Javaux, Matthieu ; Vanderborght, Jan ; Vereecken, Harry JF - Computers & Geosciences. 34 (2008), H. 12 Y1 - 2008 SN - 0098-3004 SP - 1958 EP - 1963 ER - TY - JOUR A1 - Baringhaus, Ludwig A1 - Gaigall, Daniel T1 - On Hotelling’s T² test in a special paired sample case JF - Communications in Statistics - Theory and Methods N2 - In a special paired sample case, Hotelling’s T² test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given. KW - complete block symmetry KW - Hotelling’s T² test KW - likelihood ratio test KW - uniformly most powerful invariant test Y1 - 2017 U6 - http://dx.doi.org/10.1080/03610926.2017.1408828 SN - 1532-415X VL - 48 IS - 2 SP - 257 EP - 267 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Stulpe, Werner A1 - Bugajski, S. A1 - Hellwig, K.-E. T1 - On Fuzzy Random Variables and Statistical Maps. Bugajski, S.; Hellwig, K.-E.; Stulpe, W. JF - Reports on Mathematical Physics. 41 (1998), H. 1 Y1 - 1998 SN - 0034-4877 SP - 1 EP - 11 ER - TY - CHAP A1 - Gaigall, Daniel T1 - On Consistent Hypothesis Testing In General Hilbert Spaces N2 - Inference on the basis of high-dimensional and functional data are two topics which are discussed frequently in the current statistical literature. A possibility to include both topics in a single approach is working on a very general space for the underlying observations, such as a separable Hilbert space. We propose a general method for consistently hypothesis testing on the basis of random variables with values in separable Hilbert spaces. We avoid concerns with the curse of dimensionality due to a projection idea. We apply well-known test statistics from nonparametric inference to the projected data and integrate over all projections from a specific set and with respect to suitable probability measures. In contrast to classical methods, which are applicable for real-valued random variables or random vectors of dimensions lower than the sample size, the tests can be applied to random vectors of dimensions larger than the sample size or even to functional and high-dimensional data. In general, resampling procedures such as bootstrap or permutation are suitable to determine critical values. The idea can be extended to the case of incomplete observations. Moreover, we develop an efficient algorithm for implementing the method. Examples are given for testing goodness-of-fit in a one-sample situation in [1] or for testing marginal homogeneity on the basis of a paired sample in [2]. Here, the test statistics in use can be seen as generalizations of the well-known Cramérvon-Mises test statistics in the one-sample and two-samples case. The treatment of other testing problems is possible as well. By using the theory of U-statistics, for instance, asymptotic null distributions of the test statistics are obtained as the sample size tends to infinity. Standard continuity assumptions ensure the asymptotic exactness of the tests under the null hypothesis and that the tests detect any alternative in the limit. Simulation studies demonstrate size and power of the tests in the finite sample case, confirm the theoretical findings, and are used for the comparison with concurring procedures. A possible application of the general approach is inference for stock market returns, also in high data frequencies. In the field of empirical finance, statistical inference of stock market prices usually takes place on the basis of related log-returns as data. In the classical models for stock prices, i.e., the exponential Lévy model, Black-Scholes model, and Merton model, properties such as independence and stationarity of the increments ensure an independent and identically structure of the data. Specific trends during certain periods of the stock price processes can cause complications in this regard. In fact, our approach can compensate those effects by the treatment of the log-returns as random vectors or even as functional data. Y1 - 2022 U6 - http://dx.doi.org/10.11159/icsta22.157 N1 - Proceedings of the 4th International Conference on Statistics: Theory and Applications (ICSTA’22) Prague, Czech Republic – July 28- 30 SP - Paper No. 157 PB - Avestia Publishing CY - Orléans, Kanada ER - TY - JOUR A1 - Grotendorst, Johannes T1 - On calculating the rate of linear convergence of non-linear transformed sequences JF - Proceeding SNC '11 Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation Y1 - 2011 SN - 978-1-4503-0515-0 SP - 24 EP - 33 PB - ACM CY - New York, NY ER - TY - JOUR A1 - Baringhaus, Ludwig A1 - Gaigall, Daniel T1 - On an independence test approach to the goodness-of-fit problem JF - Journal of Multivariate Analysis N2 - Let X₁,…,Xₙ be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R²→R and g:R²→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X₁,X₂),g(X₁,X₂) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xᵢ,Xⱼ),g(Xᵢ,Xⱼ)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions. KW - Goodness-of-fit test KW - Independence test KW - Parametric bootstrap KW - Vapnik–Čhervonenkis class KW - Gamma distribution Y1 - 2015 U6 - http://dx.doi.org/10.1016/j.jmva.2015.05.013 SN - 0047-259X VL - 2015 IS - 140 SP - 193 EP - 208 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Baringhaus, Ludwig A1 - Gaigall, Daniel T1 - On an asymptotic relative efficiency concept based on expected volumes of confidence regions JF - Statistics - A Journal of Theoretical and Applied Statistic N2 - The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting. KW - Volume of confidence regions KW - asymptotic relative efficiency KW - likelihood ratio test KW - multivariate normal distribution KW - multinomial distribution Y1 - 2019 U6 - http://dx.doi.org/10.1080/02331888.2019.1683560 SN - 1029-4910 VL - 53 IS - 6 SP - 1396 EP - 1436 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Reißel, Martin T1 - On a transmission boundary-value problem for the time-harmonic Maxwell equations without displacement currents / Martin Reissel Y1 - 1992 N1 - Bericht der Arbeitsgruppe Technomathematik ; 84 ; Vorabdruck SP - 19 S. ER - TY - JOUR A1 - Reißel, Martin T1 - On a Transmission Boundary Value Problem for the Time-Harmonic Maxwell Equations without Displacement Currents / Martin Reissel JF - SIAM Journal on Mathematical Analysis. 24 (1993), H. 6 Y1 - 1993 SN - 0036-1410 SP - 1440 EP - 1457 ER -