TY  - JOUR
A1  - Gaigall, Daniel
T1  - Test for Changes in the Modeled Solvency Capital Requirement of an Internal Risk Model
JF  - ASTIN Bulletin
N2  - In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.
KW  - Bootstrap
KW  - Empirical process
KW  - Functional Delta Method
KW  - Hadamard differentiability
KW  - Paired sample
Y1  - 2021
U6  - https://doi.org/10.1017/asb.2021.20
SN  - 1783-1350
VL  - 51
IS  - 3
SP  - 813
EP  - 837
PB  - Cambridge Univ. Press
CY  - Cambridge
ER  - 
TY  - JOUR
A1  - Baringhaus, Ludwig
A1  - Gaigall, Daniel
A1  - Thiele, Jan Philipp
T1  - Statistical inference for L²-distances to uniformity
JF  - Computational Statistics
N2  - The paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for L²-distances to uniformity based on the empirical distribution function, the integrated empirical distribution function and the integrated empirical survival function. Approximations of power functions, confidence intervals for the L²-distances and statistical neighbourhood-of-uniformity validation tests are obtained as main applications. The finite sample behaviour of the procedures is illustrated by a simulation study.
KW  - Integrated empirical distribution (survival) function
KW  - Goodness-of-fit tests for uniformity
KW  - Numerical inversion of Laplace transforms
KW  - Coverage probability
KW  - Equivalence test
Y1  - 2018
U6  - https://doi.org/10.1007/s00180-018-0820-0
SN  - 1613-9658
VL  - 2018
IS  - 33
SP  - 1863
EP  - 1896
PB  - Springer
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Schöning, Michael Josef
A1  - Bronder, Thomas
A1  - Wu, Chunsheng
A1  - Scheja, Sabrina
A1  - Jessing, Max
A1  - Metzger-Boddien, Christoph
A1  - Keusgen, Michael
A1  - Poghossian, Arshak
T1  - Label-Free DNA Detection with Capacitive Field-Effect Devices—Challenges and Opportunities
JF  - Proceedings
N2  - Field-effect EIS (electrolyte-insulator-semiconductor) sensors modified with a positively charged weak polyelectrolyte layer have been applied for the electrical detection of DNA (deoxyribonucleic acid) immobilization and hybridization by the intrinsic molecular charge. The EIS sensors are able to detect the existence of target DNA amplicons in PCR (polymerase chain reaction) samples and thus, can be used as tool for a quick verification of DNA amplification and the successful PCR process. Due to their miniaturized setup, compatibility with advanced micro- and nanotechnologies, and ability to detect biomolecules by their intrinsic molecular charge, those sensors can serve as possible platform for the development of label-free DNA chips. Possible application fields as well as challenges and limitations will be discussed.
Y1  - 2017
U6  - https://doi.org/10.3390/proceedings1080719
SN  - 2504-3900
N1  - This article belongs to the Proceedings of "Proceedings of the 5th International Symposium on Sensor Science (I3S 2017)"
VL  - 1
IS  - 8
SP  - Artikel 719
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Gaigall, Daniel
T1  - Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data
JF  - Metrika
N2  - We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
KW  - Marginal homogeneity test
KW  - Crámer–von-Mises distance
KW  - Paired sample
KW  - Incomplete data
KW  - Resampling test
Y1  - 2019
U6  - https://doi.org/10.1007/s00184-019-00742-5
SN  - 1435-926X
VL  - 2020
IS  - 83
SP  - 437
EP  - 465
PB  - Springer
ER  - 
TY  - JOUR
A1  - Richter, Charlotte
A1  - Braunstein, Bjoern
A1  - Winnard, Andrew
A1  - Nasser, Mona
A1  - Weber, T.
T1  - Human Biomechanical and Cardiopulmonary Responses to Partial Gravity – A Systematic Review
JF  - Frontiers in physiology
Y1  - 2017
U6  - https://doi.org/10.3389/fphys.2017.00583
IS  - 8, article 583
ER  - 
TY  - JOUR
A1  - Gaigall, Daniel
T1  - On a new approach to the multi-sample goodness-of-fit problem
JF  - Communications in Statistics - Simulation and Computation
N2  - Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.
KW  - Goodness-of-fit test
KW  - Multi-sample problem
KW  - Parametric bootstrap
Y1  - 2019
U6  - https://doi.org/10.1080/03610918.2019.1618472
SN  - 1532-4141
VL  - 53
IS  - 10
SP  - 2971
EP  - 2989
PB  - Taylor & Francis
CY  - London
ER  - 
TY  - JOUR
A1  - Laack, Walter van
T1  - Our world is well ordered in measurement and number : or why natural constants are as they are
JF  - American Journal of Humanities and Social Sciences (AHSS)
N2  - All the important natural constants can be logically explained with and derived from the first four ordinal numbers, 1, 2, 3 and 4, its addition to ten and finally the standard values for obviously maximal feasibility Ω and the optimum in our world, the Golden Section (GS), i.e. the number sequences 273 and 618. They both are the first three numbers of irrational results by an arithmetical transformation of simple geometrical relationships by creating multiplicity out of singularity. Both of them show that the infinite is inherent in finiteness and explain in a simple way the smallest deviations and fluctuations between the physical AS-IS state and the obvious spiritual ideal behind: Wherever we look in this world, and especially in important key-positions, we regularly find these sequences. All of the above mentioned numbers so seem to be key players in our world, what can be demonstrated by the derivation of natural constants.
Y1  - 2013
U6  - https://doi.org/10.11634/232907811301390
SN  - 2329-079X
SN  - 2329-0781
VL  - 1
IS  - 4
SP  - 219
EP  - 221
ER  - 
TY  - JOUR
A1  - Bronder, Thomas
A1  - Jessing, Max P.
A1  - Poghossian, Arshak
A1  - Keusgen, Michael
A1  - Schöning, Michael Josef
T1  - Detection of PCR-Amplified Tuberculosis DNA Fragments with Polyelectrolyte-Modified Field-Effect Sensors
JF  - Analytical Chemistry
N2  - Field-effect-based electrolyte-insulator-semiconductor (EIS) sensors were modified with a bilayer of positively charged weak polyelectrolyte (poly(allylamine hydrochloride) (PAH)) and probe single-stranded DNA (ssDNA) and are used for the detection of complementary single-stranded target DNA (cDNA) in different test solutions. The sensing mechanism is based on the detection of the intrinsic molecular charge of target cDNA molecules after the hybridization event between cDNA and immobilized probe ssDNA. The test solutions contain synthetic cDNA oligonucleotides (with a sequence of tuberculosis mycobacteria genome) or PCR-amplified DNA (which origins from a template DNA strand that has been extracted from Mycobacterium avium paratuberculosis-spiked human sputum samples), respectively. Sensor responses up to 41 mV have been measured for the test solutions with DNA, while only small signals of ∼5 mV were detected for solutions without DNA. The lower detection limit of the EIS sensors was ∼0.3 nM, and the sensitivity was ∼7.2 mV/decade. Fluorescence experiments using SybrGreen I fluorescence dye support the electrochemical results.
Y1  - 2018
U6  - https://doi.org/10.1021/acs.analchem.8b01807
SN  - 0003-2700
VL  - 90
IS  - 12
SP  - 7747
EP  - 7753
PB  - ACS Publications
CY  - Washington, DC
ER  - 
TY  - JOUR
A1  - Ditzhaus, Marc
A1  - Gaigall, Daniel
T1  - A consistent goodness-of-fit test for huge dimensional and functional data
JF  - Journal of Nonparametric Statistics
N2  - A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
KW  - Cramér-von-Mises statistic
KW  - separable Hilbert space
KW  - huge dimensional data
KW  - functional data
Y1  - 2018
U6  - https://doi.org/10.1080/10485252.2018.1486402
SN  - 1029-0311
VL  - 30
IS  - 4
SP  - 834
EP  - 859
PB  - Taylor & Francis
CY  - Abingdon
ER  - 
TY  - JOUR
A1  - Gaigall, Daniel
A1  - Gerstenberg, Julian
A1  - Trinh, Thi Thu Ha
T1  - Empirical process of concomitants for partly categorial data and applications in statistics
JF  - Bernoulli
N2  - On the basis of independent and identically distributed bivariate random vectors, where the components are categorial and continuous variables, respectively, the related concomitants, also called induced order statistic, are considered. The main theoretical result is a functional central limit theorem for the empirical process of the concomitants in a triangular array setting. A natural application is hypothesis testing. An independence test and a two-sample test are investigated in detail. The fairly general setting enables limit results under local alternatives and bootstrap samples. For the comparison with existing tests from the literature simulation studies are conducted. The empirical results obtained confirm the theoretical findings.
KW  - bootstrap
KW  - Categorial variable
KW  - Concomitant
KW  - Empirical process
KW  - Independence test
Y1  - 2022
U6  - https://doi.org/10.3150/21-BEJ1367
SN  - 1573-9759
VL  - 28
IS  - 2
SP  - 803
EP  - 829
PB  - International Statistical Institute
CY  - Den Haag, NL
ER  -