Accurate and Precise Zinc Isotope Ratio Measurements in Urban Aerosols

We developed an analytical method and constrained procedural boundary conditions that enable accurate and precise Zn isotope ratio measurements in urban aerosols. We also demonstrate the potential of this new isotope system for air pollutant source tracing. The procedural blank is around 5 ng and significantly lower than published methods due to a tailored ion chromatographic separation. Accurate mass bias correction using external correction with Cu is limited to Zn sample content of approximately 50 ng due to the combined effect of blank contribution of Cu and Zn from the ion exchange procedure and the need to maintain a Cu/Zn ratio of approximately 1. Mass bias is corrected for by applying the common analyte internal standardization method approach. Comparison with other mass bias correction methods demonstrates the accuracy of the method. The average precision of delta(66)Zn determinations in aerosols is around 0.05% per atomic mass unit. The method was tested on aerosols collected in Sin Paulo City, Brazil. The measurements reveal significant variations in delta(66)Zn(Imperial) ranging between -0.96 and -0.37% in coarse and between -1.04 and 0.02% in fine particular matter. This variability suggests that Zn isotopic compositions distinguish atmospheric sources. The isotopic light signature suggests traffic as the main source. We present further delta(66)Zn(Imperial) data for the standard reference material NIST SRM 2783 (delta 66Z(Imperial) = 0.26 +/- 0.10%).

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.