Sur les tests lisses d'ajustement dans le context des series chronologiques

La plupart des modèles en statistique classique repose sur une hypothèse sur la distribution des données ou sur une distribution sous-jacente aux données. La validité de cette hypothèse permet de faire de l’inférence, de construire des intervalles de confiance ou encore de tester la fiabilité du modèle. La problématique des tests d’ajustement vise à s’assurer de la conformité ou de la cohérence de l’hypothèse avec les données disponibles. Dans la présente thèse, nous proposons des tests d’ajustement à la loi normale dans le cadre des séries chronologiques univariées et vectorielles. Nous nous sommes limités à une classe de séries chronologiques linéaires, à savoir les modèles autorégressifs à moyenne mobile (ARMA ou VARMA dans le cas vectoriel). Dans un premier temps, au cas univarié, nous proposons une généralisation du travail de Ducharme et Lafaye de Micheaux (2004) dans le cas où la moyenne est inconnue et estimée. Nous avons estimé les paramètres par une méthode rarement utilisée dans la littérature et pourtant asymptotiquement efficace. En effet, nous avons rigoureusement montré que l’estimateur proposé par Brockwell et Davis (1991, section 10.8) converge presque sûrement vers la vraie valeur inconnue du paramètre. De plus, nous fournissons une preuve rigoureuse de l’inversibilité de la matrice des variances et des covariances de la statistique de test à partir de certaines propriétés d’algèbre linéaire. Le résultat s’applique aussi au cas où la moyenne est supposée connue et égale à zéro. Enfin, nous proposons une méthode de sélection de la dimension de la famille d’alternatives de type AIC, et nous étudions les propriétés asymptotiques de cette méthode. L’outil proposé ici est basé sur une famille spécifique de polynômes orthogonaux, à savoir les polynômes de Legendre. Dans un second temps, dans le cas vectoriel, nous proposons un test d’ajustement pour les modèles autorégressifs à moyenne mobile avec une paramétrisation structurée. La paramétrisation structurée permet de réduire le nombre élevé de paramètres dans ces modèles ou encore de tenir compte de certaines contraintes particulières. Ce projet inclut le cas standard d’absence de paramétrisation. Le test que nous proposons s’applique à une famille quelconque de fonctions orthogonales. Nous illustrons cela dans le cas particulier des polynômes de Legendre et d’Hermite. Dans le cas particulier des polynômes d’Hermite, nous montrons que le test obtenu est invariant aux transformations affines et qu’il est en fait une généralisation de nombreux tests existants dans la littérature. Ce projet peut être vu comme une généralisation du premier dans trois directions, notamment le passage de l’univarié au multivarié ; le choix d’une famille quelconque de fonctions orthogonales ; et enfin la possibilité de spécifier des relations ou des contraintes dans la formulation VARMA. Nous avons procédé dans chacun des projets à une étude de simulation afin d’évaluer le niveau et la puissance des tests proposés ainsi que de les comparer aux tests existants. De plus des applications aux données réelles sont fournies. Nous avons appliqué les tests à la prévision de la température moyenne annuelle du globe terrestre (univarié), ainsi qu’aux données relatives au marché du travail canadien (bivarié). Ces travaux ont été exposés à plusieurs congrès (voir par exemple Tagne, Duchesne et Lafaye de Micheaux (2013a, 2013b, 2014) pour plus de détails). Un article basé sur le premier projet est également soumis dans une revue avec comité de lecture (Voir Duchesne, Lafaye de Micheaux et Tagne (2016)).

Standardized reporting using CODES (Crash Outcome Data Evaluation System).

National Highway Traffic Safety Administration, Washington, D.C.

Expert systems for crash data collection.

Federal Highway Administration, Office of Safety and Traffic Operations, Washington, D.C.

Instrumentation for measuring pavement-vehicle interaction. Volume II: Digalog Systems operation and maintenance manual, data acquisition system, model DLI 203. Final report.

Federal Highway Administration, Structures and Applied Mechanics Division, Washington, D.C.

The crash outcome data evaluation system (CODES).

National Highway Traffic Safety Administration, Office of Research and Development, Washington, D.C.

National Traffic Data Acquisition Conference (NATDAC '94). Proceedings, volume I. Final report.

Federal Highway Administration, Washington, D.C.

National Traffic Data Acquisition Conference (NATDAC '94). Proceedings, volume II. Final report.

Federal Highway Administration, Washington, D.C.

Heavy truck data in Virginia: collection, uses, and needs. Final report.

Virginia Department of Transportation, Richmond

Development of roadside safety data collection plan. Final report.

Federal Highway Administration, Office of Safety and Traffic Operations Research and Development, McLean, Va.

National Governors' Association Truck Accident Data Collection Program - officer's manual. Final report.

Federal Highway Administration, Washington, D.C.

Skilled nursing facilities : available data show average nursing staff time changed little after Medicare payment increase : report to congressional committees.

"GAO-03-176."

OMERACT-OARSI Initiative: Osteoarthritis Research Society International set of responder criteria for osteoarthritis clinical trials revisited.

Background: The OARSI Standing Committee for Clinical Trials Response Criteria Initiative had developed two sets of responder criteria to present the results of changes after treatment in three symptomatic domains (pain, function, and patient's global assessment) as a single variable for clinical trials (1). For each domain, a response was defined by both a relative and an absolute change, with different cut-offs with regard to the drug, the route of administration and the OA localization. Objective: To propose a simplified set of responder criteria with a similar cut-off, whatever the drug, the route or the OA localization. Methods: Data driven approach: (1) Two databases were considered The 'elaboration' database with which the formal OARSI sets of responder criteria were elaborated and The 'revisit' database. (2) Six different scenarios were evaluated: The two formal OARSI sets of criteria Four proposed scenarios of simplified sets of criteria Data from clinical randomized blinded placebo controlled trials were used to evaluate the performances of the two formal scenarios with two different databases ('elaboration' versus 'revisit') and those of the four proposed simplified scenarios within the 'revisit' database. The placebo effect, active effect, treatment effect, and the required sample arm size to obtain the placebo effect and the active treatment effect observed were the performances evaluated for each of the six scenarios. Experts' opinion approach: Results were discussed among the participants of the OMERACT VI meeting, who voted to select the definite OMERACT-OARSI set of criteria (one of the six evaluated scenarios). Results: Data driven approach: Fourteen trials totaling 1886 CA patients and fifteen studies involving 8164 CA patients were evaluated in the 'elaboration' and the 'revisit' databases respectively. The variability of the performances observed in the 'revisit' database when using the different simplified scenarios was similar to that observed between the two databases ('elaboration' versus 'revisit') when using the formal scenarios. The treatment effect and the required sample arm size were similar for each set of criteria. Experts' opinion approach: According to the experts, these two previous performances were the most important of an optimal set of responder criteria. They chose the set of criteria considering both pain and function as evaluation domain and requiring an absolute change and a relative change from baseline to define a response, with similar cut-offs whatever the drug, the route of administration or the CA localization. Conclusion: This data driven and experts' opinion approach is the basis for proposing an optimal simplified set of responder criteria for CA clinical trials. Other studies, using other sets of CA patients, are required in order to further validate this proposed OMERACT - OARSI set of criteria. (C) 2004 OsteoArthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

Large scale experiments on gravel and mixed beaches: Experimental procedure, data documentation and initial results

This paper provides information on the experimental set-up, data collection methods and results to date for the project Large scale modelling of coarse grained beaches, undertaken at the Large Wave Channel (GWK) of FZK in Hannover by an international group of researchers in Spring 2002. The main objective of the experiments was to provide full scale measurements of cross-shore processes on gravel and mixed beaches for the verification and further development of cross-shore numerical models of gravel and mixed sediment beaches. Identical random and regular wave tests were undertaken for a gravel beach and a mixed sand/gravel beach set up in the flume. Measurements included profile development, water surface elevation along the flume, internal pressures in the swash zone, piezometric head levels within the beach, run-up, flow velocities in the surf-zone and sediment size distributions. The purpose of the paper is to present to the scientific community the experimental procedure, a summary of the data collected, some initial results, as well as a brief outline of the on-going research being carried out with the data by different research groups. The experimental data is available to all the scientific community following submission of a statement of objectives, specification of data requirements and an agreement to abide with the GWK and EU protocols. (C) 2005 Elsevier B.V. All rights reserved.

Quantifying the pathology of neurodegenerative disorders:Quantitative measurements, sampling strategies and data analysis

The use of quantitative methods has become increasingly important in the study of neurodegenerative disease. Disorders such as Alzheimer's disease (AD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This article reviews the advantages and limitations of the different methods of quantifying the abundance of pathological lesions in histological sections, including estimates of density, frequency, coverage, and the use of semiquantitative scores. The major sampling methods by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are also described. In addition, the data analysis methods commonly used to analyse quantitative data in neuropathology, including analyses of variance (ANOVA) and principal components analysis (PCA), are discussed. These methods are illustrated with reference to particular problems in the pathological diagnosis of AD and dementia with Lewy bodies (DLB).

Causality and synchronisation in complex systems with applications to neuroscience

This thesis presents an investigation, of synchronisation and causality, motivated by problems in computational neuroscience. The thesis addresses both theoretical and practical signal processing issues regarding the estimation of interdependence from a set of multivariate data generated by a complex underlying dynamical system. This topic is driven by a series of problems in neuroscience, which represents the principal background motive behind the material in this work. The underlying system is the human brain and the generative process of the data is based on modern electromagnetic neuroimaging methods . In this thesis, the underlying functional of the brain mechanisms are derived from the recent mathematical formalism of dynamical systems in complex networks. This is justified principally on the grounds of the complex hierarchical and multiscale nature of the brain and it offers new methods of analysis to model its emergent phenomena. A fundamental approach to study the neural activity is to investigate the connectivity pattern developed by the brain’s complex network. Three types of connectivity are important to study: 1) anatomical connectivity refering to the physical links forming the topology of the brain network; 2) effective connectivity concerning with the way the neural elements communicate with each other using the brain’s anatomical structure, through phenomena of synchronisation and information transfer; 3) functional connectivity, presenting an epistemic concept which alludes to the interdependence between data measured from the brain network. The main contribution of this thesis is to present, apply and discuss novel algorithms of functional connectivities, which are designed to extract different specific aspects of interaction between the underlying generators of the data. Firstly, a univariate statistic is developed to allow for indirect assessment of synchronisation in the local network from a single time series. This approach is useful in inferring the coupling as in a local cortical area as observed by a single measurement electrode. Secondly, different existing methods of phase synchronisation are considered from the perspective of experimental data analysis and inference of coupling from observed data. These methods are designed to address the estimation of medium to long range connectivity and their differences are particularly relevant in the context of volume conduction, that is known to produce spurious detections of connectivity. Finally, an asymmetric temporal metric is introduced in order to detect the direction of the coupling between different regions of the brain. The method developed in this thesis is based on a machine learning extensions of the well known concept of Granger causality. The thesis discussion is developed alongside examples of synthetic and experimental real data. The synthetic data are simulations of complex dynamical systems with the intention to mimic the behaviour of simple cortical neural assemblies. They are helpful to test the techniques developed in this thesis. The real datasets are provided to illustrate the problem of brain connectivity in the case of important neurological disorders such as Epilepsy and Parkinson’s disease. The methods of functional connectivity in this thesis are applied to intracranial EEG recordings in order to extract features, which characterize underlying spatiotemporal dynamics before during and after an epileptic seizure and predict seizure location and onset prior to conventional electrographic signs. The methodology is also applied to a MEG dataset containing healthy, Parkinson’s and dementia subjects with the scope of distinguishing patterns of pathological from physiological connectivity.