Estimation of conditional laws given an extreme component

Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t)$ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random vector $(X,Y)$, suitably normalized, given that $X$ is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist) and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated through simulations.Comment: 32 pages, 5 figur

Exposure of young children to household water lead in the Montreal area (Canada): the potential influence of winter-to-summer changes in water lead levels on children's blood lead concentration

Drinking water represents a potential source of lead exposure. The purpose of the present study was to estimate the magnitude of winter-to-summer changes in household water lead levels (WLLs), and to predict the impact of these variations on BLLs in young children. A study was conducted from September, 2009 to March, 2010 in 305 homes, with a follow-up survey carried out from June to September 2011 in a subsample of 100 homes randomly selected. The first 1-L sample was drawn after 5 min of flushing, followed by a further 4 consecutive 1-L samples after 30 min of stagnation. Non-linear regression and general linear mixed models were used for modelling seasonal effects on WLL. The batchrun mode of Integrated Exposure Uptake Biokinetic (IEUBK) model was used to predict the impact of changes in WLL on children's blood lead levels (BLLs). The magnitude of winter-to-summer changes in average concentrations of lead corresponded to 6.55 mug/L in homes served by lead service lines (LSL+ homes) and merely 0.30 mug/L in homes without lead service lines. For stagnant samples, the value reached 10.55 mug/L in 'LSL+ homes' and remained very low (0.36 mug/L) in 'LSL- homes'. The change in the probability of BLLs >/=5 mug/dL due to winter-to-summer changes in WLL was increased from /=5 mug/dL in young children during warm months was reduced by at least 40% by flushing tap-water

Wage losses in the year after breast cancer: Extent and determinants among Canadian women

This article is available open access through the publisher’s website at the link below. © The Author 2008.Background - Wage losses after breast cancer may result in considerable financial burden. Their assessment is made more urgent because more women now participate in the workforce and because breast cancer is managed using multiple treatment modalities that could lead to long work absences. We evaluated wage losses, their determinants, and the associations between wage losses and changes for the worse in the family's financial situation among Canadian women over the first 12 months after diagnosis of early breast cancer. Methods - We conducted a prospective cohort study among women with breast cancer from eight hospitals throughout the province of Quebec. Information that permitted the calculation of wage losses and information on potential determinants of wage losses were collected by three pretested telephone interviews conducted over the year following the start of treatment. Information on medical characteristics was obtained from medical records. The main outcome was the proportion of annual wages lost because of breast cancer. Multivariable analysis of variance using the general linear model was used to identify personal, medical, and employment characteristics associated with the proportion of wages lost. All statistical tests were two-sided. Results - Among 962 eligible breast cancer patients, 800 completed all three interviews. Of these, 459 had a paying job during the month before diagnosis. On average, these working women lost 27% of their projected usual annual wages (median = 19%) after compensation received had been taken into account. Multivariable analysis showed that a higher percentage of lost wages was statistically significantly associated with a lower level of education (Ptrend = .0018), living 50 km or more from the hospital where surgery was performed (P = .070), lower social support (P = .012), having invasive disease (P = .086), receipt of chemotherapy (P < .001), self-employment (P < .001), shorter tenure in the job (Ptrend < .001), and part-time work (P < .001). Conclusion - Wage losses and their effects on financial situation constitute an important adverse consequence of breast cancer in Canada.The Canadian Breast Cancer Research Alliance, Canadian Institutes of Health Research, and Fondation de l’Université Laval

Vine copula-based asymmetry and tail dependence modeling

© Springer International Publishing AG, part of Springer Nature 2018. Financial variables such as asset returns in the massive market contain various hierarchical and horizontal relationships that form complicated dependence structures. Modeling these structures is challenging due to the stylized facts of market data. Many research works in recent decades showed that copula is an effective method to describe relations among variables. Vine structures were introduced to represent the decomposition of multivariate copula functions. However, the model construction of vine structures is still a tough problem owing to the geometrical data, conditional independent assumptions and the stylized facts. In this paper, we introduce a new bottom-to-up method to construct regular vine structures and applies the model to 12 currencies over 16 years as a case study to analyze the asymmetric and fat tail features. The out-of-sample performance of our model is evaluated by Value at Risk, a widely used industrial benchmark. The experimental results show that our model and its intrinsic design significantly outperform industry baselines, and provide financially interpretable knowledge and profound insights into the dependence structures of multi-variables with complex dependencies and characteristics

Business analytics in industry 4.0: a systematic review

Recently, the term “Industry 4.0” has emerged to characterize several Information Technology and Communication (ICT) adoptions in production processes (e.g., Internet-of-Things, implementation of digital production support information technologies). Business Analytics is often used within the Industry 4.0, thus incorporating its data intelligence (e.g., statistical analysis, predictive modelling, optimization) expert system component. In this paper, we perform a Systematic Literature Review (SLR) on the usage of Business Analytics within the Industry 4.0 concept, covering a selection of 169 papers obtained from six major scientific publication sources from 2010 to March 2020. The selected papers were first classified in three major types, namely, Practical Application, Reviews and Framework Proposal. Then, we analysed with more detail the practical application studies which were further divided into three main categories of the Gartner analytical maturity model, Descriptive Analytics, Predictive Analytics and Prescriptive Analytics. In particular, we characterized the distinct analytics studies in terms of the industry application and data context used, impact (in terms of their Technology Readiness Level) and selected data modelling method. Our SLR analysis provides a mapping of how data-based Industry 4.0 expert systems are currently used, disclosing also research gaps and future research opportunities.The work of P. Cortez was supported by FCT - Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020. We would like to thank to the three anonymous reviewers for their helpful suggestions

On the strong uniform consistency of a new kernel density estimator

kernel estimator, strong uniform consistency, sample moments,