The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies.

We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform better than estimates based on the sample covariance matrix for heavy-tailed distributions. Simulations confirmed these findings for finite-sample efficiencies. (C) 2003 Elsevier Science (USA). All rights reserved.affine equivariance; covariance and correlation matrices; efficiency; eigenvectors and eigenvalues; influence function; multivariate median; multivariate sign; robustness; multivariate location; discriminant-analysis; principal components; dispersion matrices; tests; estimators;

Influence function and asymptotic efficiency of the affine equivariant rank covariance matrix.

Visuri et al (2001) proposed and illustrated the use of the affine equivariant rank covariance matrix (RCM) in classical multivariate inference problems. The RCM was shown to be asymptotically multinormal but explicit formulas for the limiting variances and covariances were not given yet. In this paper the influence functions and the limiting variances and covariances of the RCM and the corresponding scatter estimate are derived in the multivariate elliptic case. Limiting efficiencies are given in the multivariate normal and t-distribution cases. The estimates based on the RCM are highly efficient in the multinormal case, and for heavy tailed distribution, perform better than those based on the regular covariance matrix.Efficiency;

Canonical analysis based on scatter matrices.

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix are considered in more detail. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimator and S-estimates through theoretical and simulation studies. The theory is illustrated by an example.Canonical correlations; Canonical variables; Canonical vectors; Covariance; Covariance determinant estimator; Determinant estimator; Distribution; Efficiency; Estimator; Functions; Influence function; Matrix; Scatter; Shape matrix; Sign covariance mix; Simulation; Studies; Theory; Tyler's estimate;

Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast

Solution composition and particle size effects on the dissolution and solubility of a ThO2 microstructural analogue for UO2 matrix of nuclear fuel

The objective of this study was to investigate the dissolution rate of ThO2 which was synthesised to approximate, as closely as possible, the microstructure of UO2 in a nuclear fuel matrix. The optimal sintering temperature for ThO2 pellets was found to be 1750 ℃, which produced pellets with a microstructure similar to UO2 nuclear fuel pellets, with randomly oriented grains ranging in size from 10 to 30 μm. Dissolution was conducted using ThO2 particles of different size fractions (80 to 160 μm and 2 to 4 mm) in the presence and absence of carbonate, in solutions with pH from 2 to 8 and at 80 ℃. Dissolution rates were calculated from Th released from the solid phase to solution. Particles of ThO2 were also leached with 1 M HNO3 at 80 ℃ in order to investigate the morphological changes at the particle surfaces. The concentration of Th was found to be ≥ 10–9 mol/L at pH ≤ 4, lower than the theoretical solubility of crystalline ThO2. At higher pH values, from 4 to 8, the measured concentrations (10−10 to 10–12 mol/L) were between the theoretical solubility of ThO2 and Th(OH)4. Grain boundaries were shown to exert an influence on the dissolution of ThO2 particles. Using high resolution aqueous solution analysis, these data presented here extend the current understanding of Th solubility in solutio

Canonical analysis based on scatter matrices.

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.Canonical correlations; Canonical variables; Canonical vectors; Covariance; Covariance determinant estimator; Determinant estimator; Distribution; Efficiency; Estimator; Functions; Influence function; Matrix; Principal components; Scatter; Shape matrix; Sign; Sign covariance mix; Simulation; Studies; Theory; Tyler's estimate; Variance;

Globalization, Global Governance and the Social Determinants of Health: A review of the linkages and agenda for action

The Globalization Knowledge Network (GKN) was formed in 2005 with the purpose of examining how contemporary globalization was influencing social determinants of health. It was one of nine Knowledge Networks providing evidence-informed guidance to the work of the World Health Organization’s Commission on Social Determinants of Health (2005-2008): like most of the Knowledge Networks, its operations were financed by an external funder (in this case, the International Affairs Directorate of Health Canada, Canada’s national ministry of health). The GKN conducted two face-to-face meetings to debate, discuss, outline and review its work, and produced thirteen background papers and a Final Report. These papers and the Final Report underwent extensive internal and external peer review to ensure that their findings and policy inferences accurately reflected available evidence and scholarship. This GKN publication series was prepared under the general editorship of Ronald Labonté, with assistance from Vivien Runnels and copy-editing provided by Wayne Harding. All views expressed are exclusively those of the authors. A complete list of titles in the publication series appears on the inside back cover of this monograph

Women with PCOS have an increased risk for cardiovascular disease regardless of diagnostic criteria - a prospective population-based cohort study

OBJECTIVE: Polycystic ovary syndrome (PCOS) is associated with many cardiovascular disease (CVD) risk factors, such as obesity, type 2 diabetes mellitus and hypertension. However, it remains debatable whether the presence of multiple CVD risk factors translates to increased CVD events. DESIGN: A prospective, population-based Northern Finland Birth Cohort 1966. METHODS: Individuals with an expected date of birth in 1966 in Northern Finland have been followed from birth. Women in the cohort were classified as having PCOS according to either the National Institute of Health (NIH) criteria (n = 144) or the Rotterdam criteria (n = 386) at age 31, and they were compared to women without any PCOS features. The study population was re-examined at age 46, and the incidence of major adverse cardiovascular events (MACE), including myocardial infarction (MI), stroke, heart failure and cardiovascular mortality, was recorded up to age 53. RESULTS: During the 22-year follow-up, both women with NIH-PCOS and women with Rotterdam-PCOS had a significantly higher risk for cardiovascular events than control women. The BMI-adjusted hazard ratio (HR) for MACE in the Rotterdam-PCOS group and the NIH-PCOS group was 2.33 (1.26-4.30) and 2.47 (1.18-5.17), respectively. The cumulative hazard curves in both diagnostic categories began to diverge at age 35. Regarding the individual CVD endpoints, MI was significantly more prevalent in both women with NIH-PCOS (P = .010) and women with Rotterdam-PCOS (P = .019), when compared to control women. CONCLUSIONS: PCOS should be considered a significant risk factor for CVD. Future follow-up will show how the risk of CVD events develops after menopausal age