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For short take-off and landing (STOL) aircraft, a parallel hybrid-electric propulsion system potentially offers superior performance compared to a conventional propulsion system, because the short-take-off power requirement is much higher than the cruise power requirement. This power-matching problem can be solved with a balanced hybrid propulsion system. However, there is a trade-off between wing loading, power loading, the level of hybridization, as well as range and take-off distance. An optimization method can vary design variables in such a way that a minimum of a particular objective is attained. In this paper, a comparison between the optimization results for minimum mass, minimum consumed primary energy, and minimum cost is conducted. A new initial sizing algorithm for general aviation aircraft with hybrid-electric propulsion systems is applied. This initial sizing methodology covers point performance, mission performance analysis, the weight estimation process, and cost estimation. The methodology is applied to the design of a STOL general aviation aircraft, intended for on-demand air mobility operations. The aircraft is sized to carry eight passengers over a distance of 500 km, while able to take off and land from short airstrips. Results indicate that parallel hybrid-electric propulsion systems must be considered for future STOL aircraft.
We propose the so-called chance constrained programming model of stochastic programming theory to analyze limit and shakedown loads of structures under random strength with a lognormal distribution. A dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The edge-based smoothed finite element method (ES-FEM) is used with three-node linear triangular elements.
Electrolyte-insulator-semiconductor (EIS) field-effect sensors belong to a new generation of electronic chips for biochemical sensing, enabling a direct electronic readout. The review gives an overview on recent advances and current trends in the research and development of chemical sensors and biosensors based on the capacitive field-effect EIS structure—the simplest field-effect device, which represents a biochemically sensitive capacitor. Fundamental concepts, physicochemical phenomena underlying the transduction mechanism and application of capacitive EIS sensors for the detection of pH, ion concentrations, and enzymatic reactions, as well as the label-free detection of charged molecules (nucleic acids, proteins, and polyelectrolytes) and nanoparticles, are presented and discussed.
Domain experts regularly teach novice students how to perform a task. This often requires them to adjust their behavior to the less knowledgeable audience and, hence, to behave in a more didactic manner. Eye movement modeling examples (EMMEs) are a contemporary educational tool for displaying experts’ (natural or didactic) problem-solving behavior as well as their eye movements to learners. While research on expert-novice communication mainly focused on experts’ changes in explicit, verbal communication behavior, it is as yet unclear whether and how exactly experts adjust their nonverbal behavior. This study first investigated whether and how experts change their eye movements and mouse clicks (that are displayed in EMMEs) when they perform a task naturally versus teach a task didactically. Programming experts and novices initially debugged short computer codes in a natural manner. We first characterized experts’ natural problem-solving behavior by contrasting it with that of novices. Then, we explored the changes in experts’ behavior when being subsequently instructed to model their task solution didactically. Experts became more similar to novices on measures associated with experts’ automatized processes (i.e., shorter fixation durations, fewer transitions between code and output per click on the run button when behaving didactically). This adaptation might make it easier for novices to follow or imitate the expert behavior. In contrast, experts became less similar to novices for measures associated with more strategic behavior (i.e., code reading linearity, clicks on run button) when behaving didactically.
Game-based learning is a promising approach to anti-phishing education, as it fosters motivation and can help reduce the perceived difficulty of the educational material. Over the years, several prototypes for game-based applications have been proposed, that follow different approaches in content selection, presentation, and game mechanics. In this paper, a literature and product review of existing learning games is presented. Based on research papers and accessible applications, an in-depth analysis was conducted, encompassing target groups, educational contexts, learning goals based on Bloom’s Revised Taxonomy, and learning content. As a result of this review, we created the publications on games (POG) data set for the domain of anti-phishing education. While there are games that can convey factual and conceptual knowledge, we find that most games are either unavailable, fail to convey procedural knowledge or lack technical depth. Thus, we identify potential areas of improvement for games suitable for end-users in informal learning contexts.
Impact of Battery Performance on the Initial Sizing of Hybrid-Electric General Aviation Aircraft
(2020)
Studies suggest that hybrid-electric aircraft have the potential to generate fewer emissions and be inherently quieter when compared to conventional aircraft. By operating combustion engines together with an electric propulsion system, synergistic benefits can be obtained. However, the performance of hybrid-electric aircraft is still constrained by a battery’s energy density and discharge rate. In this paper, the influence of battery performance on the gross mass for a four-seat general aviation aircraft with a hybrid-electric propulsion system is analyzed. For this design study, a high-level approach is chosen, using an innovative initial sizing methodology to determine the minimum required aircraft mass for a specific set of requirements and constraints. Only the peak-load shaving operational strategy is analyzed. Both parallel- and serial-hybrid propulsion configurations are considered for two different missions. The specific energy of the battery pack is varied from 200 to 1,000 W⋅h/kg, while the discharge time, and thus the normalized discharge rating (C-rating), is varied between 30 min (2C discharge rate) and 2 min (30C discharge rate). With the peak-load shaving operating strategy, it is desirable for hybrid-electric aircraft to use a light, low capacity battery system to boost performance. For this case, the battery’s specific power rating proved to be of much higher importance than for full electric designs, which have high capacity batteries. Discharge ratings of 20C allow a significant take-off mass reduction aircraft. The design point moves to higher wing loadings and higher levels of hybridization if batteries with advanced technology are used.
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.
Coronavirus disease 2019 (COVID-19) is a novel human infectious disease provoked by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Currently, no specific vaccines or drugs against COVID-19 are available. Therefore, early diagnosis and treatment are essential in order to slow the virus spread and to contain the disease outbreak. Hence, new diagnostic tests and devices for virus detection in clinical samples that are faster, more accurate and reliable, easier and cost-efficient than existing ones are needed. Due to the small sizes, fast response time, label-free operation without the need for expensive and time-consuming labeling steps, the possibility of real-time and multiplexed measurements, robustness and portability (point-of-care and on-site testing), biosensors based on semiconductor field-effect devices (FEDs) are one of the most attractive platforms for an electrical detection of charged biomolecules and bioparticles by their intrinsic charge. In this review, recent advances and key developments in the field of label-free detection of viruses (including plant viruses) with various types of FEDs are presented. In recent years, however, certain plant viruses have also attracted additional interest for biosensor layouts: Their repetitive protein subunits arranged at nanometric spacing can be employed for coupling functional molecules. If used as adapters on sensor chip surfaces, they allow an efficient immobilization of analyte-specific recognition and detector elements such as antibodies and enzymes at highest surface densities. The display on plant viral bionanoparticles may also lead to long-time stabilization of sensor molecules upon repeated uses and has the potential to increase sensor performance substantially, compared to conventional layouts. This has been demonstrated in different proof-of-concept biosensor devices. Therefore, richly available plant viral particles, non-pathogenic for animals or humans, might gain novel importance if applied in receptor layers of FEDs. These perspectives are explained and discussed with regard to future detection strategies for COVID-19 and related viral diseases.
Comparative assessment of parallel-hybrid-electric propulsion systems for four different aircraft
(2020)
Until electric energy storage systems are ready to allow fully electric aircraft, the combination of combustion engine and electric motor as a hybrid-electric propulsion system seems to be a promising intermediate solution. Consequently, the design space for future aircraft is expanded considerably, as serial hybrid-electric, parallel hybrid-electric, fully electric, and conventional propulsion systems must all be considered. While the best propulsion system depends on a multitude of requirements and considerations, trends can be observed for certain types of aircraft and certain types of missions. This Paper provides insight into some factors that drive a new design toward either conventional or hybrid propulsion systems. General aviation aircraft, regional transport aircraft vertical takeoff and landing air taxis, and unmanned aerial vehicles are chosen as case studies. Typical missions for each class are considered, and the aircraft are analyzed regarding their takeoff mass and primary energy consumption. For these case studies, a high-level approach is chosen, using an initial sizing methodology. Only parallel-hybrid-electric powertrains are taken into account. Aeropropulsive interaction effects are neglected. Results indicate that hybrid-electric propulsion systems should be considered if the propulsion system is sized by short-duration power constraints. However, if the propulsion system is sized by a continuous power requirement, hybrid-electric systems offer hardly any benefit.
Häufig bremsen geringe IT-Ressourcen, fehlende Softwareschnittstellen oder eine veraltete und komplex gewachsene Systemlandschaft die Automatisierung von Geschäftsprozessen. Robotic Process Automation (RPA) ist eine vielversprechende Methode, um Geschäftsprozesse oberflächenbasiert und ohne größere Systemeingriffe zu automatisieren und Medienbrüche abzubauen. Die Auswahl der passenden Prozesse ist dabei für den Erfolg von RPA-Projekten entscheidend. Der vorliegende Beitrag liefert dafür Selektionskriterien, die aus einer qualitativen Inhaltanalyse von elf Interviews mit RPA-Experten aus dem Versicherungsumfeld resultieren. Das Ergebnis umfasst eine gewichtetet Liste von sieben Dimensionen und 51 Prozesskriterien, welche die Automatisierung mit Softwarerobotern begünstigen bzw. deren Nichterfüllung eine Umsetzung erschweren oder sogar verhindern. Die drei wichtigsten Kriterien zur Auswahl von Geschäftsprozessen für die Automatisierung mittels RPA umfassen die Entlastung der an dem Prozess mitwirkenden Mitarbeiter (Arbeitnehmerüberlastung), die Ausführbarkeit des Prozesses mittels Regeln (Regelbasierte Prozessteuerung) sowie ein positiver Kosten-Nutzen-Vergleich. Praktiker können diese Kriterien verwenden, um eine systematische Auswahl von RPA-relevanten Prozessen vorzunehmen. Aus wissenschaftlicher Perspektive stellen die Ergebnisse eine Grundlage zur Erklärung des Erfolgs und Misserfolgs von RPA-Projekten dar.
The movement of magnetic beads due to a magnetic field gradient is of great interest in different application fields. In this report we present a technique based on a magnetic tweezers setup to measure the velocity factor of magnetically actuated individual superparamagnetic beads in a fluidic environment. Several beads can be tracked simultaneously in order to gain and improve statistics. Furthermore we show our results for different beads with hydrodynamic diameters between 200 and 1000 nm from diverse manufacturers. These measurement data can, for example, be used to determine design parameters for a magnetic separation system, like maximum flow rate and minimum separation time, or to select suitable beads for fixed experimental requirements.
For performing point-of-care molecular diagnostics, magnetic immunoassays constitute a promising alternative to established enzyme-linked immunosorbent assays (ELISA) because they are fast, robust and sensitive. Simultaneous detection of multiple biomolecular targets from one body fluid sample is desired. The aim of this work is to show that multiplex magnetic immunodetection based on magnetic frequency mixing by means of modular immunofiltration columns prepared for different targets is feasible. By calculations of the magnetic response signal, the required spacing between the modules was determined. Immunofiltration columns were manufactured by 3D printing and antibody immobilization was performed in a batch approach. It was shown experimentally that two different target molecules in a sample solution could be individually detected in a single assaying step with magnetic measurements of the corresponding immobilization filters. The arrangement order of the filters and of a negative control did not influence the results. Thus, a simple and reliable approach to multi-target magnetic immunodetection was demonstrated.
Bacterial cell appendix formation supports cell-cell interaction, cell adhesion and cell movement. Additionally, in bioelectrochemical systems (BES), cell appendages have been shown to participate in extracellular electron transfer. In this work, the cell appendix formation of Clostridium acetobutylicum in biofilms of a BES are imaged and compared with conventional biofilms. Under all observed conditions, the cells possess filamentous appendages with a higher number and density in the BES. Differences in the amount of extracellular polymeric substance in the biofilms of the electrodes lead to the conclusion that the cathode can be used as electron donor and the anode as electron acceptor by C. acetobutylicum. When using conductive atomic force microscopy, a current response of about 15 nA is found for the cell appendages from the BES. This is the first report of conductivity for clostridial cell appendices and represents the basis for further studies on their role for biofilm formation and electron transfer.
Kyphoplasty of Osteoporotic Fractured Vertebrae: A Finite Element Analysis about Two Types of Cement
(2019)
Thermal and Optical Study on the Frequency Dependence of an Atmospheric Microwave Argon Plasma Jet
(2019)
Heating efficiency of magnetic nanoparticles decreases with gradual immobilization in hydrogels
(2019)
Monitoring the cellular metabolism of bacteria in (bio)fermentation processes is crucial to control and steer them, and to prevent undesired disturbances linked to metabolically inactive microorganisms. In this context, cell-based biosensors can play an important role to improve the quality and increase the yield of such processes. This work describes the simultaneous analysis of the metabolic behavior of three different types of bacteria by means of a differential light-addressable potentiometric sensor (LAPS) set-up. The study includes Lactobacillus brevis, Corynebacterium glutamicum, and Escherichia coli, which are often applied in fermentation processes in bioreactors. Differential measurements were carried out to compensate undesirable influences such as sensor signal drift, and pH value variation during the measurements. Furthermore, calibration curves of the cellular metabolism were established as a function of the glucose concentration or cell number variation with all three model microorganisms. In this context, simultaneous (bio)sensing with the multi-organism LAPS-based set-up can open new possibilities for a cost-effective, rapid detection of the extracellular acidification of bacteria on a single sensor chip. It can be applied to evaluate the metabolic response of bacteria populations in a (bio)fermentation process, for instance, in the biogas fermentation process.
Enzyme-catalyzed reactions have been designed to mimic various Boolean logic gates in the general framework of unconventional biomolecular computing. While some of the logic gates, particularly OR, AND, are easy to realize with biocatalytic reactions and have been reported in numerous publications, some other, like NXOR, are very challenging and have not been realized yet with enzyme reactions. The paper reports on a novel approach to mimicking the NXOR logic gate using the bell-shaped enzyme activity dependent on pH values. Shifting pH from the optimum value to the acidic or basic values by using acid or base inputs (meaning 1,0 and 0,1 inputs) inhibits the enzyme reaction, while keeping the optimum pH (assuming 0,0 and 1,1 input combinations) preserves a high enzyme activity. The challenging part of the present approach is the selection of an enzyme with a well-demonstrated bell-shape activity dependence on the pH value. While many enzymes can satisfy this condition, we selected pyrroloquinoline quinone (PQQ)-dependent glucose dehydrogenase as this enzyme has the optimum pH center-located on the pH scale allowing the enzyme activity change by the acidic and basic pH shift from the optimum value corresponding to the highest activity. The present NXOR gate is added to the biomolecular “toolbox” as a new example of Boolean logic gates based on enzyme reactions.
Im Rahmen der Digitalisierung ist die zunehmende Automatisierung von bisher manuellen Prozessschritten ein Aspekt, der massive Auswirkungen auf die zukünftige Arbeitswelt haben wird. In diesem Kontext werden an den Einsatz von Softwarerobotern zur Prozessautomatisierung hohe Erwartungen geknüpft. Bei den Implementierungsansätzen wird die Diskussion aktuell insbesondere durch Robotic Process Automation (RPA) und Chatbots geprägt. Beide Ansätze verfolgen das gemeinsame Ziel einer 1:1-Automatisierung von menschlichen Handlungen und dadurch ein direktes Ersetzen von Mitarbeitern durch Maschinen. Bei RPA werden Prozesse durch Softwareroboter erlernt und automatisiert ausgeführt. Dabei emulieren RPA-Roboter die Eingaben auf der bestehenden Präsentationsschicht, so dass keine Änderungen an vorhandenen Anwendungssystemen notwendig sind. Am Markt werden bereits unterschiedliche RPA-Lösungen als Softwareprodukte angeboten. Durch Chatbots werden Ein- und Ausgaben von Anwendungssystemen über natürliche Sprache realisiert. Dadurch ist die Automatisierung von unternehmensexterner Kommunikation (z. B. mit Kunden) aber auch von unternehmensinternen Assistenztätigkeiten möglich. Der Beitrag diskutiert die Auswirkungen von Softwarerobotern auf die Arbeitswelt anhand von Anwendungsbeispielen und erläutert die unternehmensindividuelle Entscheidung über den Einsatz von Softwarerobotern anhand von Effektivitäts- und Effizienzzielen.
Hydrogen peroxide (H2O2) is a typical surface sterilization agent for packaging materials used in the pharmaceutical, food and beverage industries. We use the finite-elements method to analyze the conceptual design of an in-line thermal evaporation unit to produce a heated gas mixture of air and evaporated H2O2 solution. For the numerical model, the required phase-transition variables of pure H2O2 solution and of the aerosol mixture are acquired from vapor-liquid equilibrium (VLE) diagrams derived from vapor-pressure formulations. This work combines homogeneous single-phase turbulent flow with heat-transfer physics to describe the operation of the evaporation unit. We introduce the apparent heat-capacity concept to approximate the non-isothermal phase-transition process of the H2O2-containing aerosol. Empirical and analytical functions are defined to represent the temperature- and pressure-dependent material properties of the aqueous H2O2 solution, the aerosol and the gas mixture. To validate the numerical model, the simulation results are compared to experimental data on the heating power required to produce the gas mixture. This shows good agreement with the deviations below 10%. Experimental observations on the formation of deposits due to the evaporation of stabilized H2O2 solution fits the prediction made from simulation results.
A light-addressable potentiometric sensor (LAPS) is a field-effect-based (bio-) chemical sensor, in which a desired sensing area on the sensor surface can be defined by illumination. Light addressability can be used to visualize the concentration and spatial distribution of the target molecules, e.g., H+ ions. This unique feature has great potential for the label-free imaging of the metabolic activity of living organisms. The cultivation of those organisms needs specially tailored surface properties of the sensor. O2 plasma treatment is an attractive and promising tool for rapid surface engineering. However, the potential impacts of the technique are carefully investigated for the sensors that suffer from plasma-induced damage. Herein, a LAPS with a Ta2O5 pH-sensitive surface is successfully patterned by plasma treatment, and its effects are investigated by contact angle and scanning LAPS measurements. The plasma duration of 30 s (30 W) is found to be the threshold value, where excessive wettability begins. Furthermore, this treatment approach causes moderate plasma-induced damage, which can be reduced by thermal annealing (10 min at 300 °C). These findings provide a useful guideline to support future studies, where the LAPS surface is desired to be more hydrophilic by O2 plasma treatment.
Tribological performance of biodegradable lubricants under different surface roughness of tools
(2019)
Digital Image Correlation (DIC) is a powerful tool used to evaluate displacements and deformations in a non-intrusive manner. By comparing two images, one of the undeformed reference state of a specimen and another of the deformed target state, the relative displacement between those two states is determined. DIC is well known and often used for post-processing analysis of in-plane displacements and deformation of specimen. Increasing the analysis speed to enable real-time DIC analysis will be beneficial and extend the field of use of this technique.
Here we tested several combinations of the most common DIC methods in combination with different parallelization approaches in MATLAB and evaluated their performance to determine whether real-time analysis is possible with these methods. To reflect improvements in computing technology different hardware settings were also analysed. We found that implementation problems can reduce the efficiency of a theoretically superior algorithm such that it becomes practically slower than a suboptimal algorithm. The Newton-Raphson algorithm in combination with a modified Particle Swarm algorithm in parallel image computation was found to be most effective. This is contrary to theory, suggesting that the inverse-compositional Gauss-Newton algorithm is superior. As expected, the Brute Force Search algorithm is the least effective method. We also found that the correct choice of parallelization tasks is crucial to achieve improvements in computing speed. A poorly chosen parallelisation approach with high parallel overhead leads to inferior performance. Finally, irrespective of the computing mode the correct choice of combinations of integerpixel and sub-pixel search algorithms is decisive for an efficient analysis. Using currently available hardware realtime analysis at high framerates remains an aspiration.
Production and Characterization of Porous Fibroin Scaffolds for Regenerative Medical Application
(2019)
Neuromuscular strength training of the leg extensor muscles plays an important role in the rehabilitation and prevention of age and wealth related diseases. In this paper, we focus on the design and implementation of a Cartesian admittance control scheme for isotonic training, i.e. leg extension and flexion against a predefined weight. For preliminary testing and validation of the designed algorithm an experimental research and development platform consisting of an
industrial robot and a force plate mounted at its end-effector has been used. Linear, diagonal and arbitrary two-dimensional motion trajectories with different weights for the leg extension and flexion part are applied. The proposed algorithm is easily adaptable to trajectories consisting of arbitrary six-dimensional poses and allows the implementation of individualized trajectories.
Training-induced increase in Achilles tendon stiffness affects tendon strain pattern during running
(2019)
Background
During the stance phase of running, the elasticity of the Achilles tendon enables the utilisation of elastic energy and allows beneficial contractile conditions for the triceps surae muscles. However, the effect of changes in tendon mechanical properties induced by chronic loading is still poorly understood. We tested the hypothesis that a training-induced increase in Achilles tendon stiffness would result in reduced tendon strain during the stance phase of running, which would reduce fascicle strains in the triceps surae muscles, particularly in the mono-articular soleus.
Methods
Eleven subjects were assigned to a training group performing isometric singleleg plantarflexion contractions three times per week for ten weeks, and another ten subjects formed a control group. Before and after the training period, Achilles tendon stiffness was estimated, and muscle-tendon mechanics were assessed during running at preferred speed using ultrasonography, kinematics and kinetics.
Results
Achilles tendon stiffness increased by 18% (P <0:01) in the training group, but the associated reduction in strain seen during isometric contractions was not statistically significant. Tendon elongation during the stance phase of running was similar after training, but tendon recoil was reduced by 30% (P <0:01), while estimated tendon force remained unchanged. Neither gastrocnemius medialis nor soleus fascicle shortening during stance was affected by training.
Discussion
These results show that a training-induced increase in Achilles tendon
stiffness altered tendon behaviour during running. Despite training-induced changes in tendon mechanical properties and recoil behaviour, the data suggest that fascicle shortening patterns were preserved for the running speed that we examined. The asymmetrical changes in tendon strain patterns supports the notion that simple inseries models do not fully explain the mechanical output of the muscle-tendon unit during a complex task like running.
In modern bioanalytical methods, it is often desired to detect several targets in one sample within one measurement. Immunological methods including those that use superparamagnetic beads are an important group of techniques for these applications. The goal of this work is to investigate the feasibility of simultaneously detecting different superparamagnetic beads acting as markers using the magnetic frequency mixing technique. The frequency of the magnetic excitation field is scanned while the lower driving frequency is kept constant. Due to the particles’ nonlinear magnetization, mixing frequencies are generated. To record their amplitude and phase information, a direct digitization of the pickup-coil’s signal with subsequent Fast Fourier Transformation is performed. By synchronizing both magnetic beads using frequency scanning in magnetic frequency mixing technique magnetic fields, a stable phase information is gained. In this research, it is shown that the amplitude of the dominant mixing component is proportional to the amount of superparamagnetic beads inside a sample. Additionally, it is shown that the phase does not show this behaviour. Excitation frequency scans of different bead types were performed, showing different phases, without correlation to their diverse amplitudes. Two commercially available beads were selected and a determination of their amount in a mixture is performed as a demonstration for multiplex measurements.
Sensitive and rapid detection of cholera toxin subunit B using magnetic frequency mixing detection
(2019)
Cholera is a life-threatening disease caused by the cholera toxin (CT) as produced by some Vibrio cholerae serogroups. In this research we present a method which directly detects the toxin’s B subunit (CTB) in drinking water. For this purpose we performed a magnetic sandwich immunoassay inside a 3D immunofiltration column. We used two different commercially available antibodies to capture CTB and for binding to superparamagnetic beads. ELISA experiments were performed to select the antibody combination. The beads act as labels for the magnetic frequency mixing detection technique. We show that the limit of detection depends on the type of magnetic beads. A nonlinear Hill curve was fitted to the calibration measurements by means of a custom-written python software. We achieved a sensitive and rapid detection of CTB within a broad concentration range from 0.2 ng/ml to more
than 700 ng/ml.
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.
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.