Adaptive wavelet based estimator of the memory parameter for stationary Gaussian processes

This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish a central limit theorem for the estimator of the memory parameter with the minimax rate of convergence (up to a logarithm factor). The quality of the estimators are attested by simulations

Adaptive semiparametric wavelet estimator and goodness-of-fit test for long memory linear processes

International audienceThis paper is first devoted to study an adaptive wavelet based estimator of the long memory parameter for linear processes in a general semi-parametric frame. This is an extension of Bardet {\it et al.} (2008) which only concerned Gaussian processes. Moreover, the definition of the long memory parameter estimator is modified and asymptotic results are improved even in the Gaussian case. Finally an adaptive goodness-of-fit test is also built and easy to be employed: it is a chi-square type test. Simulations confirm the interesting properties of consistency and robustness of the adaptive estimator and test

Construction de bases d'ondelettes de L2[0,1]L^2[0,1] et estimation du paramètre de longue mémoire par la méthode des ondelettes.

This study is devoted to the use of wavelets in two different fields, constructions of bases on the interval and long-memory parameter estimation. In the first part we present general constructions of orthogonal and biorthogonal multiresolution analyses on the interval. In the first one, we describe a direct method to define an orthonormal multiresolution analysis. In the second one, we use the integration and derivation method for constructing a biorthogonal multiresolution analysis. As applications, we prove that these analyses are adapted to study regular functions on the interval (H^{s}([0,1])$et$H^{s}_{0}([0,1])$for$s\in\mathbb{N}$). The second part is devoted to the study of adaptive wavelet-based estimators of the long-memory parameter for Gaussian then linear processes in a general semiparametric frame. We introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish central limit theorems for the estimators of the memory parameter with the minimax rate of convergence (up to a logarithm factor). Finally adaptive goodness-of-fit tests are also built and easy to be employed: they are chi-square type tests. Simulations confirm the interesting properties of consistency and robustness of the adaptive estimators and tests.Cette thèse est consacrée à l'utilisation des ondelettes dans deux domaines à savoir la construction de bases sur l'intervalle et l'estimation du paramètre de longue mémoire par transformée (discrète) d'ondelettes. Dans un premier volet Nous présentons des constructions générales d'analyses multirésolution orthogonales (par une méthode directe) et biorthogonale sur l'intervalle (par la méthode d'intégration et de dérivation) .Comme applications, on étudie les espaces de Sobolev$H^{s}([0,1])$et$H^{s}_{0}([0,1])$pour$s\in\mathbb{N}$ . Le second volet est consacré à l'estimation du paramètre de longues ondelettes (non issues d'une analyse multirésolution) dans un cadre semi paramétrique. Les processus stationnaires à longue mémoire considérés sont du type gaussien puis linéaire. Pour chaque type de processus, on construit un estimateur adaptatif vérifiant un théorème limite central à vitesse de convergence au sens du minimax (à un logarithme prés). Les qualités statistiques de ces estimateurs (robustesses et consistances) sont vérifiées par des simulations et enfin un test d'adéquation est établi (considéré comme un test de longue mémoire dans le cas linéaire)

More general constructions of wavelets on the interval

Accessible en ligne : http://www.commun-math-anal.org/vv4.htmInternational audienceIn this paper we present general constructions of orthogonal and biorthogonal multiresolution analysis on the interval. In the first one, we describe a direct method to define an orthonormal multiresolution analysis. In the second one, we use the integration and derivation method for constructing a biorthogonal multiresolution analysis. As applications, we prove that these analyses are adapted to study regular functions on the interval

The Genomic Grade Assay Compared With Ki67 to Determine Risk of Distant Breast Cancer Recurrence

The Genomic Grade Index (GGI) was previously developed, evaluated on frozen tissue, and shown to be prognostic in early breast cancer. To test the GGI in formalin-fixed, paraffin-embedded breast cancer tumors, a quantitative reverse transcriptase polymerase chain reaction assay was developed and named the Genomic Grade (GG). The GG assay has the potential to increase the clinical application of the GGI, but robust demonstration of the clinical validity of the GG assay is required.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Injury burden in individuals aged 50 years or older in the Eastern Mediterranean region, 1990–2019: a systematic analysis from the Global Burden of Disease Study 2019

Background: Injury poses a major threat to health and longevity in adults aged 50 years or older. The increased life expectancy in the Eastern Mediterranean region warrants a further understanding of the ageing population's inevitable changing health demands and challenges. We aimed to examine injury-related morbidity and mortality among adults aged 50 years or older in 22 Eastern Mediterranean countries. Methods: Drawing on data from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019, we categorised the population into adults aged 50–69 years and adults aged 70 years and older. We examined estimates for transport injuries, self-harm injuries, and unintentional injuries for both age groups, with sex differences reported, and analysed the percentage changes from 1990 to 2019. We reported injury-related mortality rates and disability-adjusted life-years (DALYs). The Socio-demographic Index (SDI) and the Healthcare Access and Quality (HAQ) Index were used to better understand the association of socioeconomic factors and health-care system performance, respectively, with injuries and health status in older people. Healthy life expectancy (HALE) was compared with injury-related deaths and DALYs and to the SDI and HAQ Index to understand the effect of injuries on healthy ageing. Finally, risk factors for injury deaths between 1990 and 2019 were assessed. 95% uncertainty intervals (UIs) are given for all estimates. Findings: Estimated injury mortality rates in the Eastern Mediterranean region exceeded the global rates in 2019, with higher injury mortality rates in males than in females for both age groups. Transport injuries were the leading cause of deaths in adults aged 50–69 years (43·0 [95% UI 31·0–51·8] per 100 000 population) and in adults aged 70 years or older (66·2 [52·5–75·5] per 100 000 population), closely followed by conflict and terrorism for both age groups (10·2 [9·3–11·3] deaths per 100 000 population for 50–69 years and 45·7 [41·5–50·3] deaths per 100 000 population for ≥70 years). The highest annual percentage change in mortality rates due to injury was observed in Afghanistan among people aged 70 years or older (400·4% increase; mortality rate 1109·7 [1017·7–1214·7] per 100 000 population). The leading cause of DALYs was transport injuries for people aged 50–69 years (1798·8 [1394·1–2116·0] per 100 000 population) and unintentional injuries for those aged 70 years or older (2013·2 [1682·2–2408·7] per 100 000 population). The estimates for HALE at 50 years and at 70 years in the Eastern Mediterranean region were lower than global estimates. Eastern Mediterranean countries with the lowest SDIs and HAQ Index values had high prevalence of injury DALYs and ranked the lowest for HALE at 50 years of age and HALE at 70 years. The leading injury mortality risk factors were occupational exposure in people aged 50–69 years and low bone mineral density in those aged 70 years or older. Interpretation: Injuries still pose a real threat to people aged 50 years or older living in the Eastern Mediterranean region, mainly due to transport and violence-related injuries. Dedicated efforts should be implemented to devise injury prevention strategies that are appropriate for older adults and cost-effective injury programmes tailored to the needs and resources of local health-care systems, and to curtail injury-associated risk and promote healthy ageing. Funding: Bill & Melinda Gates Foundation