On locally optimal nonparametric tests

Summary There is an abundancy of problems in which no parametric model realistically describes the situation and in which, accordingly, we have to resort to nonparametric methods. As the numerical problems connected with nonparametric tests are becoming less and less important, rank tests, permutation tests and the like are becoming more and more part of the standard armatory of applied statisticians. The lack of tabulated critical values, for instance, should no longer be a serious objection against the use of permutation tests in practice; cf. Edgington (1987).The rationale underlying permutation and rank tests has been outlined in quite a number of text books and papers; cf. Fraser (1957), Lehmann (1959), Hájek-Sidák (1967) or Witting (1970). Roughly speaking, permutation tests are constructibel if the data can be condensed by means of a sufficient and complete statistic allowing for the proper kind of conditioning. Rank tests arise if the underlying problem is invariant with respect to (w.r.t.) a large group of transformations which leads to a maximal invariant statistic consisting of (signed) ranks.Most practical nonparametric problems, however, are too complex to be tractable by just one of those approaches. Many of them, however, can be handled by a combination of both techniques. In this paper we outline the logic underlying that combined reduction method and apply it to construct locally most powerful tests. Moreover, we discuss what we label Hoeffding's transfer problem, i.e. the uniformity aspect of locally most powerful tests with respect to the starting point at the boundary. We are concentrating on the discussion of the nonparametric two-sample location and scale problem. Further important problems are mentioned in Section III.This is a written account of an invited lecture delivered by the third author on occasion of the 14th Symposium über Operations Research, Ulm, September 6–8, 1989.     

Distribution of values of σ2 (n) in residue classes

IntegersN for which ₂ (n has weak uniform distribution (modN) are determined.     

Ein Algorithmus zur Lösung eines Verteilungsproblems

Zusammenfassung Bei der Lastverteilung eines Elektrizitätsversorgungsunternehmens besteht die Möglichkeit, durch eine Tonfrequenzrundsteueranlage die Last optimal aufzuteilen. Eine Zielsetzung besteht darin, durch Zu- und Wegschalten von Verbrauchergruppen die Lastspitze möglichst klein zu halten. Dabei muß allerdings jedem Verbraucher in einem gewissen Zeitraum eine gewisse Einschaltdauer garantiert sein. Der zur Lösung herangezogene Algorithmus basiert im wesentlichen auf dem Prinzip der dynamischen Optimierung und der Idee von Branch- and-Bound-Verfahren.

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Summary One aim of electric load management is to keep load peaks low by switching on and off water heaters of different groups of customers. There is a restriction that those heaters have to be switched on within a certain period of time for some fixed time. The optimal switching strategy for this distribution problem is computed using dynamic programming and the idea of branch and bound methods.

     

Stereochemical analysis of isopentenyl diphosphate isomerase type II from Staphylococcus aureus using chemically synthesized (S)- and (R)-[2-2H]isopentenyl diphosphates

[chemical reaction: see text]. To study the catalysis of isopentenyl diphosphate (IPP) isomerase type II from Staphylococcus aureus, which is a flavoprotein catalyzing the interconversion of IPP and dimethylallyl diphosphate, we have chemically synthesized (S)- and (R)-[2-2H]IPP and carried out stereochemical analysis of the reaction. Our results show that the C-2 deprotonation of IPP by this enzyme is pro-R stereospecific, suggesting a similar stereochemical course as the type I enzyme.     

1H-NMR-spektroskopische Analyse von 2-Chlor-1.3.2-dioxarsolan

The¹H-NMR-spectral data of 2-chloro-1.3.2-dioxarsolane are presented and discussed. The protons of the methylene groups form in concentrated solutions by rapide chlorine exchange anAAAA spin system. In dilute solutions the protons form anAABB spin system, which is changed to anAAAA system by addition of chlorine ions.The vicinal H–C–C–H-coupling constants indicate a twist-envelope conformation.

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Resonance type dielectric behavior in solids

Experimental evidence now indicates that the microwave dielectric properties of solids are strongly influenced by the infrared active phonon modes. The “real dielectric constant”, ε′, of polar materials, i. e. those in which ?′ is noticeably greater than the square of the optical index of refraction, exhibits a temperature dependence dominated by the change of integrated infrared absorption. The microwave dielectric loss, ?″, is influenced by the low frequency “tail” of the infrared resonance type absorption, as may be inferred from the monotonic increase with temperature and proportionality to frequency. It is suggested that the one dimensional coupling of the electric field to the acoustic modes of a dielectric solid would lead to additional low frequency “background” dielectric losses which are essentially frequency independent, in agreement with experimental observations.     

Mass resolved MPI spectra of methyl iodide in the 430-490 nm region

The mass resolved multiphoton ionization (MPI) spectra of methyl iodide were obtained in the 430-490 nm region using a time-of-flight (TOF) mass spectrometer. They have the same vibrational structure, which testifies that the fragment species, in the wavelength region under study, are from the photodissociation of multiphoton ionized molecular parent ions. Some features in the spectra are identified as three-photon excitations to 6p and 7s Rydberg states of methyl iodide. Two new vibrational structures of some Rydberg states are observed. The mechanism of ionization and dissociation is also discussed.     

Electrochemical investigation of redox thermodynamics of immobilized myoglobin: ionic and ligation effects

In this study, we investigated redox thermodynamics of myoglobin as well as the ionic (phosphate ions) and ligation (imidazole) effects via a dynamic electrochemical approach. We employed a previously established system that features nonmediated, direct electrochemistry of myoglobin and myoglobin in an immobilized state (i.e., diffusionless electrochemistry). Thermodynamics parameters were obtained by measuring redox potential (E degrees ') of myoglobin at varied temperature (T), in the presence and in the absence of specific ions or axial ligands. As a step further, we evaluated contributions from allosteric effect and axial iron ligation by partitioning E degrees ' changes into entropic and enthalpic terms. Compensation phenomena between the entropic and enthalpic changes were observed in all these cases. On the basis of these studies, we also correlated these phenomena to possible structural variations.