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- 2023 (4) (remove)
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- Conductive Boundary Condition (1)
- Cramér-von-Mises test (1)
- Human factors (1)
- Inverse Scattering (1)
- Transmission Eigenvalues (1)
- adaptive systems (1)
- assistance system (1)
- central symmetry test (1)
- conditional excess distribution (1)
- confidence interval (1)
- exchangeability test (1)
- gamification (1)
- goodness-of-fit test (1)
- independence test (1)
- manufacturing (1)
- not identically distributed (1)
- random effects (1)
On the applicability of several tests to models with not identically distributed random effects
(2023)
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.
Assistance systems have been widely adopted in the manufacturing sector to facilitate various processes and tasks in production environments. However, existing systems are mostly equipped with rigid functional logic and do not provide individual user experiences or adapt to their capabilities. This work integrates human factors in assistance systems by adjusting the hardware and instruction presented to the workers’ cognitive and physical demands. A modular system architecture is designed accordingly, which allows a flexible component exchange according to the user and the work task. Gamification, the use of game elements in non-gaming contexts, has been further adopted in this work to provide level-based instructions and personalised feedback. The developed framework is validated by applying it to a manual workstation for industrial assembly routines.
The Cramér-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, quantiles of the new limit distributions are given and new bootstrap techniques for approximation purposes are introduced and justified. The results motivate new one-sample goodness-of-fit tests for the distribution of the excess over a confidence level and a new confidence interval for the related fitting error. Simulation studies investigate size and power of the tests as well as coverage probabilities of the confidence interval in the finite sample case. A practice-oriented application of the Cramér-von-Mises tests is the determination of an appropriate confidence level for the fitting approach. The adoption of the idea to the well-known problem of threshold detection in the context of peaks over threshold modelling is sketched and illustrated by data examples.
In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.