Robust estimation via minimum distance methods

Summary Given a fixed parametric family {P } it is desired to estimate. However, due to contaminations of various sorts, the data actually collected by the statistician follow a distribution that is close to, but possibly distinct from, theP 's. It is proved that, under these conditions and in an appropriate asymptotic framework, the minimum distance estimators of the Cramér-von Mises type are robust. Specification of a Cramér-von Mises weight functionH defines a notion of distance; each such choice ofH then delineates the kind of contamination possible, and leads to an estimator which defends optimally against it. When the theory is specialized to location models, various choices ofH lead to estimators asymptotically equivalent to such familiar ones as trimmed mean, median, Hodges-Lehmann estimator, and so forth. The framework developed herein provides some guidelines for choosing among the possible estimators, and suggests that the standard Cramér-von Mises estimator of location is probably as good a robust estimator as any.Supported by NSF grant MCS 75-10376     

Unit radius and the resolution of inverse square law forces

An equation for the solution of inverse square law forces that arise in rectilinear systems from gravitational, electrical, and magnetic fields, produced by complex multibody or multielement sources, is derived from a concept known asunit radius, which is associated with orbital systems, and the use of this equation in computer evaluation of simple models such as disks and spheres shows results that are in good agreement with those predicted by classical methods using a somewhat indirect approach. Additionally, these results show that, within the profile of the model so analyzed, the effective distance between the reference point and the resultant source is equal in all cases to the radius of the model, and that—again within the profile of the model—the magnitude of the resultant source varies directly with the distance of the reference point from the center of the model. Theproximity effect of sources of appreciable dimensions is examined in some detail and there is good evidence to show that as a result of this effect the resultant force when measured at the perimeter of a two-dimensional disk-shaped source is some 23% lower than the value anticipated by classical theory.     

The micro-determination of carbon and hydrogen in organic compounds containing phosphorus

Several reagents have been examined for use in the micro-determination of carbon and hydrogen in organic compounds containing phosphorus for which low carbon values had previously been reported. Tungstic oxide was found to be the most convenient reagent for this purpose. A modification of the procedure of Friedrich was used throughout this investigation which is suitable for universal application.     

The determination of chromium in low-alloy irons and steels by atomic absorption spectrophotometry

An atomic absorption spectrophotometric procedure for the determination of 0.001–0.50% chromium in low-alloy iron and steel is described. The sample is dissolved in phosphoric-sulphuric acid before atomisation. The method is rapid, preliminary separations are not required and the accuracy obtained with standard samples is well within the permissible range for routine determinations.     

The micro-determination of carbon and hydrogen in fluorine-containing organic compounds

Summary The sample is burned in a silica combustion tube, using a 4 ml per minute oxygen stream. Oxidation of the combustion products is completed by passing them over a platinum contact heated to 750°C, after the manner ofFriedrich. Silver wool at the same temperature removes sulphur and halogens, including the fluorine from any hydrogen fluoride produced, and granular sodium fluoride at about 270°C is used to absorb silicon tetrafluoride.The water vapour and carbon dioxide are determined in the usual way by absorption in magnesium perchlorate and soda-asbestos respectively. Satisfactory results have been obtained for the analyses of 4 mg samples of compounds containing the elements C, H, O, F, the standard deviation of the results for hydrogen being about ±0,1% H and for carbon being about ±0,2% C.Preliminary work indicates that fluorocarbons may be analysed if water-vapour is introduced into the system, and that the presence of nitrogen in compounds presents no difficulty when an external absorbent for nitrogen oxides is used. Certain refinements are included, which are applicable to the conventional apparatus for micro carbon and hydrogen determination.

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Zusammenfassung Zur Bestimmung von Kohlenstoff und Wasserstoff in fluorhaltigen organischen Verbindungen wird die Substanz in einem Quarzverbrennungsrohr im Sauerstoffstrom von 4 ml/Minute verbrannt. Die vollständige Oxydation der Verbrennungsprodukte erfolgt nachFriedrich durch Überleiten über einen Platinkontakt bei 750°C. Bei derselben Temperatur hält Silberwolle Schwefel und alle Halogene einschließlich Fluor zurück, soweit es als Fluorwasserstoff vorliegt. Zur Absorption von Siliciumtetrafluorid wird gekörntes Natriumfluorid bei etwa 270°C verwendet.Wasserdampf und Kohlendioxyd werden in der üblichen Weise mittels Magnesiumperchlorat bzw. Natronasbest bestimmt. Bei Einwaagen von 4 mg Substanz irgendeiner Verbindung der Elemente C, H, O und F werden befriedigende Ergebnisse erhalten. Die durchschnittlichen Abweichungen von der Theorie betragen für Wasserstoff etwa ±0,1%, bei Kohlenstoff etwa ±0,2%.Vorversuche haben gezeigt, daß fluorhältige Kohlenwasserstoffe bei gleichzeitiger Zufuhr von Wasserdampf in die Apparatur analysiert werden können und daß die Gegenwart von Stickstoff in der Analysensubstanz keine Schwierigkeiten mit sich bringt, wenn ein zusätzliches Absorptionsmittel für Stickstoffoxyde vorgesehen ist. Einige Verbesserungen der herkömmlichen Apparatur für die Mikro-C-H-Bestimmung werden angeführt.

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Résumé L'échantillon est brûlé dans un tube à combustion en silice, utilisant un débit d'oxygène de 4 ml par minute. L'oxydation des produits de combustion se complète en les faisant passer sur un contact de platine chauffé à 750° C d'après le procédé deFriedrich. La laine d'argent à la même température élimine le soufre et les halogènes y compris le fluor de tout fluorure produit et le fluorure de sodium granulaire à 270° environ sert à absorber le tétrafluorure de silicium.La vapeur d'eau et le gaz carbonique sont dosés comme d'habitude par absorption sur le perchlorate de magnésium et l'amiante sodé respectivement. Des résultats satisfaisants ont été obtenus pour les analyses de 4 mg d'échantillons de composés contenant les éléments C, H, O, F; l'erreur moyenne des résultats pour l'hydrogène étant ±0,1% H et pour le carbone, environ ± 0,2% C.Un travail préliminaire indique que les hydrocarbures fluorés peuvent être analysés si l'on introduit de la vapeur d'eau dans le système et que la présence d'azote dans les composés ne présente pas de difficulté quand on utilise un absorbant extérieur pour les oxydes de l'azote. Certaines améliorations applicables à l'appareil classique pour les microdosages de carbone et d'hydrogène sont incluses.

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With 4 Figures.     

Mercurous nitrate as a reductimetric reagent : The titration of various oxidising agents

It has been found that when excess of a solution containing ferrous ions is added to certain oxidising agents, the equivalent amount of ferric iron produced can be titrated accurately with mercurous nitrate, enabling the original oxidant to be assessed. Oxidising agents which have been determined in this way are potassium permanganate, potassium persulphate, ceric sulphate, sodium vanadate, potassium chlorate, hydrogen peroxide and potassium dichromate. The last substance provides a convenient primary standard for the standardisation of mercurous nitrate solutions.     

GBRD's: Some new constructions for difference matrices,generalised hadamard matrices and balanced generalised weighing matrices

A new construction is given for difference matrices. The generalized Hadamard matrices GH(q(q – 1)²; EA(q)) are constructed whenq andq – 1 are both prime powers. Other generalised Hadamard matrices are also shown to exist. For example, there exist GH(n; G) forn = 5² 2 3, 2⁶ 3², 11² 2² 3, 17² 2 3², 53² 2 3³, 71² 2² 3², 107² 2² 3³, 149² 5² 2 3,.... Finally, a new construction for the BGW ((q ⁴ – 1)/(q – 1),q ³,q ²(q – 1);q _q-1), and a construction for the new BGW ((q ⁸ – 1)/(q ² – 1),q ⁶,q ⁴(q ² – 1);G) are given, wheneverq is a prime power, andG is a group of orderq + 1.     

On the determination of 36Cl and 129I in solid materials from nuclear decommissioning activities

Journal of Radioanalytical and Nuclear Chemistry - Determination of the 36Cl and 129I massic activities using pyrolysis combined with radiochemical separation (using a Cl-resin) in concrete and...     

Rapid on-site radionuclide screening of aqueous waste streams using dip-stick technologies and liquid scintillation counting

Journal of Radioanalytical and Nuclear Chemistry - This paper describes an early-stage evaluation of a purpose-designed extraction/detection system that can be deployed by non-specialists either...     

A rigorous lower bound for the stability regions of the quadratic map

We establish a lower bound on the measure of the set of stable parameters a for the quadratic map Q_a(x)=ax(1−x). For these parameters, we prove that Q_a either has a single stable periodic orbit or a period-doubling bifurcation. From this result, we also obtain a non-trivial upper bound on the set of stochastic parameters for Q_a.