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.     

Charge transport in a mixed ionically/electronically conducting, cationic, polyacetylene ionomer between ion-blocking electrodes

The electrical behavior of the cationic, polyacetylene-based, conjugated ionomer, poly[(2-cyclooctatetraenylethyl)trimethylammonium trifluoromethanesulfonate], sandwiched between gold electrodes is reported. The steady-state current of this mixed ionically/electronically conducting system is assigned to be unipolar diffusive hole transport for voltages below approximately 1.4 V, giving way to bipolar migratory transport above approximately 1.4 V. In the low-voltage regime, a non-Faradaically controlled doping model is proposed where p-doping at the anode is balanced by the charging of an ionic double layer at the cathode. In the high-voltage regime, n- and p-type regions extend from the electrodes as the voltage becomes sufficient to drive disproportionation and the electric field required by the redistribution of ions begins to substantially influence carrier transport. The assignment of a transport mechanism is primarily based on analyzing the decay of the steady-state system under short-circuit and open-circuit conditions. First, it is shown that the power describing the power-law decay of the short-circuit current is characteristic of the steady-state carrier profile. Second, it is argued that a component of the time-dependent, open-circuit voltage decaying more rapidly than the time scale for ion motion is indicative of a substantial migratory component to steady-state transport, as observed in the high-voltage regime. The hole and electron mobilities are estimated to be on the order of 10(-7)-10(-6) cm(2) V(-1) s(-1).     

Analysis of the Thomas-Fermi-von Weizsäcker equation for an infinite atom without electron repulsion

The equation $$\left\{ { - \Delta + |\psi (x)|^{2p - 2} - |x|^{ - 1} } \right\}\psi (x) = 0$$ in three dimensions is investigated. Uniqueness and other properties of the positive solution are proved for 3/2<p<2. There are two physical interpretations of this equation forp=5/3: (i) As the TFW equation for an infinite atomwithout electron repulsion; (ii) The positive solution, ψ, suitably scaled, is asymptotically equal to the solution of the TFW equation for an atom or moleculewith electron repulsion in the regime where the nuclear charges are large andx is close to one of the nuclei.     

Über siliciumaromatische Verbindungen. III. Trimethylsilyl- und Triphenylsilyl-substituierte Farbstoffe der Anthrachinonreihe

The influence of the presence of trimethylsilyl and triphenylsilyl groups in substituents of anthraquinone on the properties of anthraquinone vat, acid, and dispersion dyes was investigated.     

Spectrophotometric determination of thallium as thallium tetriodide

Iodide ions react with thallic ions at pH 2–8 to form a complex iodide, which is suitable for the spectrophotometric determination of thallium. The reaction has a sensitivity of 0.05 μg Tl per cm² for log $\text{I}{}_0\text{I}$ = 0.001 and obeys Beer's law up to 40 p.p.m. Optimum conditions for the reaction have been established. The standard deviation is 0.6%. The effects of temperature and pH, the ratio of thallium to reagent, stability of the complex, its conformity to Beer's law, and the rate of color formation were studied. The effect of many diverse ions was examined.     

Photometrische Mikrobestimmung der Kohlehydrate

Zusammenfassung Es wird eine photometrische Mikromethode zur Bestimmung der Kohlehydrate beschrieben.Die Methode beruht auf der charakteristischen Farbreaktion, die die Kohlehydrate mit konz. Schwefelsäure und-Naphthol geben (Molischsche Reaktion).Durch die Wahl optimaler Reaktionsbedingungen wurde die Empfindlichkeit der Reaktion so gesteigert, daß sich noch 25 Kohlehydrate mit ausreichender Genauigkeit quantitativ bestimmen lassen.Die Methode, die sich durch Einfachheit und Zuverlässigkeit auszeichnet, eignet sich besonders für die Mikrobestimmung von Kohlehydraten in biologischen Flüssigkeiten wie Blut und Liquor.

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Résumé (W) On décrit une microméthode photométrique pour la détermination des hydrates de carbone.La méthode repose sur la réaction colorée caractéristique que donnent les hydrates de carbone avec l'acide sulfurique concentré et l'-naphtol (réaction deMolisch).Grâce au choix des meilleures conditions, la sensibilité de la réaction a été poussée de telle sorte que l'on peut encore déterminer quantitativement avec une précision absolue 25 d'hydrates de carbone. Le procédé qui se distingue par sa simplicité et sa sûreté, se prête particulièrement à la microdétermination des hydrates de carbone dans les liquides biologiques comme le sang et le sérum.

     

Rock porosity determination by combination of X-ray computerized tomography with mercury porosimetry

First results are described of coupling of mercury porosimetry with X-ray computerized tomography (CT) as a new combination technique for rock porosity studies. This technique is suitable for rock samples with a pronounced mercury intrusion-extrusion hysteresis and includes CT measurements before and after mercury intrusion. The entrapped portion of mercury, when the pressure after the intrusion into the rock sample is reduced to 0.1 MPa, serves as a contrast agent in the porous network to localize spatial distribution of rock porosity by CT. The results obtained show that the mercury intrusion and therefore the porosity were quite different for the separate mineral phases. Therefore the combination of mercury porosimetry and computer tomography can give 3-D data on mineral-specific porosity distributions with additional pore size information. In contrast to mercury porosimetry as a single method, results of the combination technique with CT represent a direct visualization of porosity variation and do not depend on any special pore network model. Received: 2 July 1996 / Revised: 20 November 1996 / Accepted: 22 November 1996