The bootstrap: Some large sample theory and connections with robustness

The bootstrap, discussed by Efron (1979, 1981), is a powerful tool for the nonparametric estimation of sampling distributions and asymptotic standard errors. We demonstrate consistency of the bootstrap distribution estimates for a general class of robust differentiable statistical functionals. Our conditions for consistency of the bootstrap are variants of previously considered criteria for robustness of the associated statistics. A general example shows that, for almost any location statistic, consistency of the bootstrap variance estimator requires a tail condition on the distribution from which samples are taken. A modification of Efron's estimator of standard error is shown to circumvent this problem.     

Production of hair intercomparison materials for use in population monitoring programmes for mercury and methylmercury exposure

Ten kilograms of hair obtained from India were used as the basis for two intercomparison materials, one with natural low levels of mercury and methylmercury, and one with an elevated level of methylmercury. The latter was produced by labeling the hair with a solution containing methylmercury. To convert the hair into homogeneous powders, cryogenic milling was utilized. 70% of the final material passed through a 0.075 mm sieve. Subsequent studies were carried out to establish the homogeneity of the materials and the stability of the methylmercury label. The materials will be distributed in an international intercomparison, the results from which will be used to obtain recommended values for total mercury and methylmercury.     

Determination of minor and trace elements in Turkish diet by duplicate portion technique

The minor and trace element content of diet samples from two different social population groups were determined. Samples were prepared by duplicate portion technique by colecting everything 16 subjects ate and drank during a 3-day period. Samples were homogenized, freeze-dried and elemental concentrations of Br, Co, Cr, Cs, Fe, K, Na, Rb, Sc, Se and Zn were determined by instrumental neutron activation analysis. Elemental concentrations and daily dietary intake of the elements were compared with the diets of other nations.     

What is an atom in a molecule?

The derivation of the Hirshfeld atoms in molecules from information theory is clarified. The importance for chemistry of the concept of atoms in molecules (AIM) is stressed, and it is argued that this concept, while highly useful, constitutes a noumenon in the sense of Kant.     

The significance of hair mineral analysis as a means for assessing internal body burdens of environmental pollutants: Results from an IAEA Co-ordinated Research Programme

During a five-year period, the International Atomic Energy Agency supported a Coordinated Research Programme (CRP) to investigate the quantitative relationship between internal body burdens of a number of elements of environmental health significance and their respective concentrations in hair. The use of nuclear-related analytical techniques, such as neutron activation analysis, X-ray fluorescence, particle-induced X-ray emission and radiotracers, was emphasized. One aspect of the CRP focused on studies in man, using autopsy cases, of mineral distribution in five tissues, i.e. liver, kidney, lung, brain and bone in addition to hair, and the elements of primary importance were As, Cd, Cu, Hg, Pb, Se and Zn. Emphasis was placed on analytical quality assurance. Hair and internal tissue samples were obtained from subjects from Bulgaria, China, the former German Democratic Republic, Hungary, Japan, Norway and Sweden.     

Accreditation for United States environmental laboratories

 There is currently no national program for recognition of United States environmental laboratories. This situation should change sometime in 1998 as environmental testing laboratories should be able to apply for accreditation in the United States via a system developed by the National Environmental Laboratory Accreditation Conference (NELAC). NELAC is an organization whose purpose is to establish performance standards for accrediting environmental laboratories. Laboratories to be accredited will be required to demonstrate qualifications of testing personnel, pass on-site inspections, perform satisfactorily on proficiency test samples, and meet specified quality assurance standards.     

First-order gradient correction for the exchange-energy density functional for atoms

Summary Spurred by earlier discoveries by Deb and others that a first-order correction in the kinetic energy functional leads to an improved kinetic energy, a first-order gradient term is studied as a component of the gradient-corrected functional for atomic exchange energy. This term is shown to improve the local density approximation to the exchange energy more than does the usual second-order gradient correction. The imperative of systematically deriving this gradient correction is discussed but not resolved.