Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Tracer applications of noble gas radionuclides in the geosciences

Noble gas radionuclides, including 81Kr (t1/2 = 229,000 years), 85Kr (t1/2 = 10.8 years), and 39Ar (t1/2 = 269 years), possess nearly ideal chemical and physical properties for studies of earth and environmental processes. Recent advances in Atom Trap Trace Analysis (ATTA), a laser-based atom counting method, have enabled routine measurements of the radiokrypton isotopes, as well as the demonstration of the ability to measure 39Ar in environmental samples. Here we provide an overview of the ATTA technique, and a survey of recent progress made in several laboratories worldwide.We review the application of noble gas radionuclides in the geosciences and discuss how ATTA can help advance these fields, specifically: determination of groundwater residence times using 81Kr, 85Kr, and 39Ar; dating old glacial ice using 81Kr; and an 39Ar survey of the main water masses of the oceans, to study circulation pathways and estimate mean residence times. Other scientific questions involving a deeper circulation of fluids in the Earth's crust and mantle are also within the scope of future applications. We conclude that the geoscience community would greatly benefit from an ATTA facility dedicated to this field, with instrumentation for routine measurements, as well as for research on further development of ATTA methods.

Leopold Loew : a biography ; with a transl. of some of the tributes paid to his memory on the occasion of the centenary of his birth ... 1911

by William N. Loewy

Observation and applications of single-electron charge signals in the XENON100 experiment

The XENON100 dark matter experiment uses liquid xenon in a time projection chamber (TPC) to measure xenon nuclear recoils resulting from the scattering of dark matter weakly interacting massive particles (WIMPs). In this paper, we report the observation of single-electron charge signals which are not related to WIMP interactions. These signals, which show the excellent sensitivity of the detector to small charge signals, are explained as being due to the photoionization of impurities in the liquid xenon and of the metal components inside the TPC. They are used as a unique calibration source to characterize the detector. We explain how we can infer crucial parameters for the XENON100 experiment: the secondary-scintillation gain, the extraction yield from the liquid to the gas phase and the electron drift velocity.

Overview of imlementation of some ESAPP funded projects in the HoA

Evaluation by the regional coordinator of ESAPP projects implemented in 2004.

On The Breakdown Properties of some Multivariate M-Functionals

For probability distributions on ℝq, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution-free’ M-functional of scatter is given. These include a symmetrized version of Tyler's M-functional of scatter, and the multivariate t M-functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M-functional of scatter and of its symmetrized version are 1/q and inline image, respectively. For the multivariate t M-functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/(q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low-dimensional subspaces.

Mathematical and empirical examinations of some epidemiological procedures

In epidemiology literature, it is often required to investigate the relationships between means where the levels of experiment are actually monotone sets forming a partition on the range of sampling values. With this need, the analysis of these group means is generally performed using classical analysis of variance (ANOVA). However, this method has never been challenged. In this dissertation, we will formulate and present our examination of its validity. First, the classical assumptions of normality and constant variance are not always true. Second, under the null hypothesis of equal means, the test statistic for the classical ANOVA technique is still valid. Third, when the hypothesis of equal means is rejected, the classical analysis techniques for hypotheses of contrasts are not valid. Fourth, under the alternative hypothesis, we can show that the monotone property of levels leads to the conclusion that the means are monotone. Fifth, we propose an appropriate method for handing the data in this situation. ^