Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator

AMS classifications: 62G20, 62G32;asymptotic normality;confidence intervals;Edgeworth expansions;extreme value index;Hill estimator;regular variation;tail index

Edgeworth Expansions for the Distribution Function of the Hill Estimator

We establish Edgeworth expansions for the distribution function of the centered and normalized Hill estimator for the positive extreme value index.estimation;variation;statistical distribution

Interacting electrons in polygonal quantum dots

The low-lying eigenstates of a system of two electrons confined within a two-dimensional quantum dot with a hard polygonal boundary are obtained by means of exact diagonalization. The transition from a weakly correlated charge distribution for small dots to a strongly correlated "Wigner molecule" for large dots is studied, and the behaviour at the crossover is determined. In sufficiently large dots, a recently proposed mapping to an effective charge-spin model is investigated, and is found to produce the correct ordering of the energy levels and to give a good first approximation to the size of the level spacings. We conclude that this approach is a valuable method to obtain the low energy spectrum of few-electron quantum dots

Predicting Infectious ComplicatioNs in Children with Cancer : an external validation study

Background:The aim of this study was to validate the 'Predicting Infectious ComplicatioNs in Children with Cancer' (PICNICC) clinical decision rule (CDR) that predicts microbiologically documented infection (MDI) in children with cancer and fever and neutropenia (FN). We also investigated costs associated with current FN management strategies in Australia.Methods:Demographic, episode, outcome and cost data were retrospectively collected on 650 episodes of FN. We assessed the discrimination, calibration, sensitivity and specificity of the PICNICC CDR in our cohort compared with the derivation data set.Results:Using the original variable coefficients, the CDR performed poorly. After recalibration the PICNICC CDR had an area under the receiver operating characteristic (AUC-ROC) curve of 0.638 (95% CI 0.590-0.685) and calibration slope of 0.24. The sensitivity, specificity, positive predictive value and negative predictive value of the PICNICC CDR at presentation was 78.4%, 39.8%, 28.6% and 85.7%, respectively. For bacteraemia, the sensitivity improved to 85.2% and AUC-ROC to 0.71. Application at day 2, taking into consideration the proportion of MDI known (43%), further improved the sensitivity to 87.7%. Length of stay is the main contributor to cost of FN treatment, with an average cost per day of AUD 2183 in the low-risk group.Conclusions:For prediction of any MDI, the PICNICC rule did not perform as well at presentation in our cohort as compared with the derivation study. However, for bacteraemia, the predictive ability was similar to that of the derivation study, highlighting the importance of recalibration using local data. Performance also improved after an overnight period of observation. Implementation of a low-risk pathway, using the PICNICC CDR after a short period of inpatient observation, is likely to be safe and has the potential to reduce health-care expenditure

Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator

AMS classifications: 62G20, 62G32;

Prevalence and risk of Down syndrome in monozygotic and dizygotic multiple pregnancies in Europe: implications for prenatal screening.

OBJECTIVE: To determine risk of Down syndrome (DS) in multiple relative to singleton pregnancies, and compare prenatal diagnosis rates and pregnancy outcome. DESIGN: Population-based prevalence study based on EUROCAT congenital anomaly registries. SETTING: Eight European countries. POPULATION: 14.8 million births 1990-2009; 2.89% multiple births. METHODS: DS cases included livebirths, fetal deaths from 20 weeks, and terminations of pregnancy for fetal anomaly (TOPFA). Zygosity is inferred from like/unlike sex for birth denominators, and from concordance for DS cases. MAIN OUTCOME MEASURES: Relative risk (RR) of DS per fetus/baby from multiple versus singleton pregnancies and per pregnancy in monozygotic/dizygotic versus singleton pregnancies. Proportion of prenatally diagnosed and pregnancy outcome. STATISTICAL ANALYSIS: Poisson and logistic regression stratified for maternal age, country and time. RESULTS: Overall, the adjusted (adj) RR of DS for fetus/babies from multiple versus singleton pregnancies was 0.58 (95% CI 0.53-0.62), similar for all maternal ages except for mothers over 44, for whom it was considerably lower. In 8.7% of twin pairs affected by DS, both co-twins were diagnosed with the condition. The adjRR of DS for monozygotic versus singleton pregnancies was 0.34 (95% CI 0.25-0.44) and for dizygotic versus singleton pregnancies 1.34 (95% CI 1.23-1.46). DS fetuses from multiple births were less likely to be prenatally diagnosed than singletons (adjOR 0.62 [95% CI 0.50-0.78]) and following diagnosis less likely to be TOPFA (adjOR 0.40 [95% CI 0.27-0.59]). CONCLUSIONS: The risk of DS per fetus/baby is lower in multiple than singleton pregnancies. These estimates can be used for genetic counselling and prenatal screening

CETL 2010: Enhancing Learning Experiences in Higher Education

We report on the results of integrating student response technology by Turning Point 2008©, simply referred to as clickers, into pre-service science and mathematics and education courses at the University of Southern Queensland (USQ), Australia. Many of the pre-service teachers have weak backgrounds in science and mathematics and lack confidence or interest in these subjects. This study investigated the use of clickers as a means of engaging students with science and mathematics classes and enhancing their learning outcomes. The effect of two different pedagogical uses of clickers on students’ perceptions was also explored. In the science education classes, clickers were used as tool to identify prior knowledge and prompt discussion, whereas in the mathematics education classes, the clickers were used at the end of lectures to check that learning had occurred. Surveys were conducted in the science and mathematics classes using measures of students’ perception of clickers and their contribution to overall learning. Although analyses of these data revealed positive student support for the use of clickers in enhancing student engagement and learning in both science and mathematics classes, students’ responses in the science education classes were far more positive. Further, the impact of the approach used in science education on pre-service teachers’ science teaching self-efficacy was evaluated. A pre-test and post-test in the scienceeducation class using the Science Teaching Efficacy Beliefs Instrument (STEBI) showed significant increases in science teaching selfefficacy, supporting the effectiveness of the pedagogical approach used in science