Ce travail de recherche s'inscrit dans le cadre des méthodes factorielles qui permettent de décrire et prédire des données structurées en plusieurs tableaux. Les objectifs et la nature des données d'épidémiologie analytique dans le domaine vétérinaire ont amené à centrer le travail sur les méthodes de régression multibloc, qui orientent la description de plusieurs tableaux de variables vers l'explication d'un autre tableau. Un des principaux objectifs est de contribuer à la réflexion sur la sensibilité de ces méthodes à la multicolinéarité. Des méthodes statistiques existantes sont présentées et reliées dans un cadre unifié, relevant soit de critères à maximiser comparables, soit d'un continuum général les reliant. De nouvelles méthodes peu vulnérables à l'égard de la multicolinéarité, et s'appliquant au cas de données structurées en deux puis en (K+1) tableaux, sont proposées. L'intérêt de ces méthodes, ainsi que des continuums qui leur sont associés, est illustré sur la base d'études de cas réels en épidémiologie. Ce travail de recherche a permis d'appliquer les méthodes multiblocs au domaine de l'épidémiologie animale, dans lequel elles n'avaient pas encore été utilisées.

This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies.

The objective of this research was to develop fluorescence-based tools that are suitable for performing rapid, accurate and direct characterization of natural organic matter (NOM) and colloidal/particulate substances present in natural water. Most available characterization methods are neither suitable for characterizing all the major NOM fractions such as protein-, humic acid-, fulvic acid- and polysaccharide-like substances as well as colloidal/particulate matter present in natural water nor are they suitable for rapid analyses. The individual and combined contributions of these NOM fractions and colloidal/particulate matter present in natural water contribute to membrane fouling, disinfection by-products formation and undesirable biological growth in drinking water treatment processes and distribution systems. The novel techniques developed in this research therefore, provide an avenue for improved understanding of these negative effects and proactive implementation of control and/or optimization strategies. The fluorescence excitation-emission matrix (EEM) method was used for characterization of NOM and colloidal/particulate matter present in water. Unlike most NOM and colloidal/particulate matter characterization techniques, this method can provide fast and consistent analyses with high instrumental sensitivity. The feasibility of using this method for monitoring NOM at very low concentration levels was also demonstrated with an emphasis on optimizing the instrument parameters necessary to obtain reproducible fluorescence signals. Partial least squares regression (PLS) was used to develop calibration models by correlating the fluorescence EEM intensities of water samples that contained surrogate NOM fractions with their corresponding dissolved organic carbon (DOC) concentrations. These fluorescence-based calibration models were found to be suitable for identifying/monitoring the extent of the relative changes that occur in different NOM fractions and the interactions between polysaccharide- and protein-like NOM in water treatment processes and distribution systems. Principal component analysis (PCA) of fluorescence EEMs was identified as a viable tool for monitoring the performance of biological filtration as a pre-treatment step, as well as ultrafiltration (UF) and nanofiltration (NF) membrane systems. The principal components (PCs) extracted in this approach were related to the major membrane foulant groups such as humic substances (HS), protein-like and colloidal/particulate matter in natural water. The PC score plots generated using the fluorescence EEMs obtained after just one hour of UF or NF operation could be related to high fouling events likely caused by elevated levels of colloidal/particulate-like material in the biofilter effluents. This fluorescence EEM-based PCA approach was sensitive enough to be used at low organic carbon levels present in NF permeate and has potential as an early detection method to identify high fouling events, allowing appropriate operational countermeasures to be taken. This fluorescence EEM-based PCA approach was also used to extract information relevant to reversible and irreversible membrane fouling behaviour in a bench-scale flat sheet cross flow UF process consisting of cycles of permeation and back-washing. PC score-based analysis revealed that colloidal/particulate matter mostly contributed to reversible fouling, while HS and protein-like matter were largely responsible for irreversible fouling. This method therefore has potential for monitoring modes of membrane fouling in drinking water treatment applications. The above approach was further improved by utilizing the evolution of the PC scores over the filtration time and relating these to membrane fouling by the use of PC scores??? balanced-based differential equations. Using these equations the proposed fluorescence-based modeling approach was capable of forecasting UF fouling behaviours with good accuracy based solely on fluorescence data obtained at time = 15 min from the initiation of the filtration process. In addition, this approach was tested experimentally as a basis for optimization by modifying the UF back-washing times with the objective of minimizing energy consumption and maximizing water production. Preliminary optimization results demonstrated the potential of this approach to reduce power consumption by significant percentages. This approach was also useful for identifying the fouling components of the NOM that were contributing to reversible and irreversible membrane fouling. Grand River water (Southwestern Ontario, Canada) was used as the natural water source for developing the techniques presented in this thesis. Future research focusing on testing these methods for monitoring of membrane fouling and treatment processes in large-scale drinking water treatment facilities that experience different sources of raw water would be useful for identifying the limitation of these techniques and areas for improvements.

L’analyse biomécanique du mouvement humain en utilisant des systèmes optoélectroniques et des marqueurs cutanés considère les segments du corps comme des corps rigides. Cependant, le mouvement des tissus mous par rapport à l'os, c’est à dire les muscles et le tissu adipeux, provoque le déplacement des marqueurs. Ce déplacement est le fait de deux composantes, une composante propre correspondant au mouvement aléatoire de chaque marqueur et une composante à l’unisson provoquant le déplacement commun des marqueurs cutanés lié au mouvement des masses sous-jacentes. Si nombre d’études visent à minimiser ces déplacements, des simulations ont montré que le mouvement des masses molles réduit la dynamique articulaire. Cette observation est faite uniquement par la simulation, car il n'existe pas de méthodes capables de dissocier la cinématique des masses molles de celle de l’os. L’objectif principal de cette thèse consiste à développer une méthode numérique capable de distinguer ces deux cinématiques. Le premier objectif était d'évaluer une méthode d'optimisation locale pour estimer le mouvement des masses molles par rapport à l’humérus obtenu avec une tige intra-corticale vissée chez trois sujets. Les résultats montrent que l'optimisation locale sous-estime de 50% le déplacement des marqueurs et qu’elle conduit à un classement de marqueurs différents en fonction de leur déplacement. La limite de cette méthode vient du fait qu'elle ne tient pas compte de l’ensemble des composantes du mouvement des tissus mous, notamment la composante en unisson. Le second objectif était de développer une méthode numérique qui considère toutes les composantes du mouvement des tissus mous. Plus précisément, cette méthode devait fournir une cinématique similaire et une plus grande estimation du déplacement des marqueurs par rapport aux méthodes classiques et dissocier ces composantes. Le membre inférieur est modélisé avec une chaine cinématique de 10 degrés de liberté reconstruite par optimisation globale en utilisant seulement les marqueurs placés sur le pelvis et la face médiale du tibia. L’estimation de la cinématique sans considérer les marqueurs placés sur la cuisse et le mollet permet d'éviter l’influence de leur déplacement sur la reconstruction du modèle cinématique. Cette méthode testée sur 13 sujets lors de sauts a obtenu jusqu’à 2,1 fois plus de déplacement des marqueurs en fonction de la méthode considérée en assurant des cinématiques similaires. Une approche vectorielle a montré que le déplacement des marqueurs est surtout dû à la composante à l’unisson. Une approche matricielle associant l’optimisation locale à la chaine cinématique a montré que les masses molles se déplacent principalement autour de l'axe longitudinal et le long de l'axe antéro-postérieur de l'os. L'originalité de cette thèse est de dissocier numériquement la cinématique os de celle des masses molles et les composantes de ce mouvement. Les méthodes développées dans cette thèse augmentent les connaissances sur le mouvement des masses molles et permettent d’envisager l’étude de leur effet sur la dynamique articulaire. / Biomechanical analysis of human movement using optoelectronic system and skin markers considers body segments as rigid bodies. However the soft tissue motion relative to the bone, including muscles, fat mass, results in relative displacement of markers. This displacement is the results of two components, an own component which corresponds to a random motion of each marker and an in-unison component corresponding to the common movement of skin markers resulting from the movement of the underlying wobbling mass. While most studies aim to minimize these displacements, computer simulation models have shown that the movement of the soft tissue motion relative to the bones reduces the joint kinetics. This observation is only available using computer simulations because there are no methods able to distinguish the kinematics of wobbling mass of the bones kinematics. The main objective of this thesis is to develop a numerical method able to distinguish this different kinematics. The first aim of this thesis was to assess a local optimisation method for estimating the soft tissue motion using intra-cortical pins screwed into the humerus in three subjects. The results show that local optimisation underestimates of 50% the marker displacements. Also it leads to a different marker ranking in terms of displacement. The limit of local optimisation comes from the fact that it does not consider all the components of the soft tissue motion, especially the in-unison component. The second aim of this thesis was to develop a numerical method that accounts for all the component of the soft tissue motion. More specifically, this method should provide similar kinematics and estimate large marker displacement and distinguish the two components to conventional approaches. The lower limb is modeled using a 10 degree of freedom chain model reconstructed using global optimisation and the markers placed only on the pelvis and the medial face of the shank. The original estimate of joint kinematics without considering the markers placed on the thigh and on the calf avoids the influences of these markers displacement on the kinematic model reconstruction. This method was tested on 13 subjects who performed hopping trials and obtained up to 2.1 times of marker displacement depending the method considered ensuring similar joint-kinematics. A vector approach shown that marker displacements is more induce by the in-unison component. A matrix approach combining the local optimisation and the kinematic model shown that the wobbling mass moves around the longitudinal axis and along the antero-posterior axis of the bone. The originality of this thesis is to numerically distinguish the bone kinematics from the wobbling mass kinematics and the two components of the soft tissue motion. The methods developed in this thesis increases the knowledge on soft tissue motion and allow future studies to consider their movement in joint kinetics calculation.

Call-response surveys were conducted to better delineate and estimate the population of the nationally threatened least bittern and their habitat requirements in southern Manitoba, Canada. Other marsh bird species whose populations are believed to be declining due to wetland loss throughout, or in parts of, their range were also surveyed including the American bittern, pied-billed grebe, sora, Virginia rail and yellow rail. Surveys were conducted during the 2003 and 2004 breeding seasons within 46 different wetlands. Least bitterns were encountered on 26 occasions at 15 sites within 5 wetlands. The sora was the most abundant and widely distributed target species and was encountered on 330 occasions in 39 of the 46 surveyed wetlands. Yellow rails were not detected during either survey year due to survey methodology. Use of the call-response survey protocol led to an increase in the numbers of all target species detected. This increase was more significant for the least bittern, sora and Virginia rail. Habitat was assessed as percent vegetation cover within a 50-m radius around the calling sites, and forest resource inventory data were used in a Geographic Information System to determine the landscape composition within a 500-m radius around the sites and within a 5-km radius around the wetlands surveyed. Logistic regression analyses were used to evaluate the relationship between the presence of the target species and the site and landscape characteristics. The target species responded differently to different site and landscape characteristics. Least bittern and pied-billed grebe selected areas with higher proportions of Typha spp. and tall shrubs; American bittern also selected areas with higher proportions of tall shrubs. At the 5-km scale, the American bittern responded positively to the amount of wetland and some positive trends were also detected for the pied-billed grebe. Sora and Virginia rail were not associated with any of the measured landscape characteristics. One of the most important steps towards the conservation of marsh bird species in Manitoba and elsewhere is the development, adoption, and implementation of a standardized survey protocol. Based on the results of the present study, I recommend that future surveys include both a passive and call-broadcast period for marsh bird species. Future surveys should be conducted in both the morning and evening and sites should be visited 3 times each during the breeding season. In southern Manitoba, call-response surveys should begin as early as the beginning of May to ensure the survey incorporates the period of peak vocalization. I recommend that future yellow rail surveys be conducted after dark. In this study many of the target species selected sites that had a greater area of wetland habitat surrounding them. Future wetland conservation efforts should focus on the protection and/or restoration of wetland complexes to ensure that remaining wetlands do not become smaller and increasingly isolated from one another. In addition, the Rat River Swamp was found to be the most productive marsh complex for least bittern in southern Manitoba. Measures should be taken to protect this area from future development and alteration.

This thesis studies the Second-order Least Squares (SLS) estimation method in regression models with and without measurement error. Applications of the methodology in general quasi-likelihood and variance function models, censored models, and linear and generalized linear models are examined and strong consistency and asymptotic normality are established. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is used and its asymptotic properties are studied. Finite sample performances of the estimators in all of the studied models are investigated through simulation studies.

Maximum likelihood is an ubiquitous method used in the estimation of generalized linear mixed model (GLMM). However, the method entails computational difficulties and relies on the normality assumption for random effects. We propose a second-order least squares (SLS) estimator based on the first two marginal moments of the response variables. The proposed estimator is computationally feasible and requires less distributional assumptions than the maximum likelihood estimator. To overcome the numerical difficulties of minimizing an objective function that involves multiple integrals, a simulation-based SLS estimator is proposed. We show that the SLS estimators are consistent and asymptotically normally distributed under fairly general conditions in the framework of GLMM. Missing data is almost inevitable in longitudinal studies. Problems arise if the missing data mechanism is related to the response process. This thesis develops the proposed estimators to deal with response data missing at random by either adapting the inverse probability weight method or applying the multiple imputation approach. In practice, some of the covariates are not directly observed but are measured with error. It is well-known that simply substituting a proxy variable for the unobserved covariate in the model will generally lead to biased and inconsistent estimates. We propose the instrumental variable method for the consistent estimation of GLMM with covariate measurement error. The proposed approach does not need any parametric assumption on the distribution of the unknown covariates. This makes the method less restrictive than other methods that rely on either a parametric distribution of the covariates, or to estimate the distribution using some extra information. In the presence of data outliers, it is a concern that the SLS estimators may be vulnerable due to the second-order moments. We investigated the robustness property of the SLS estimators using their influence functions. We showed that the proposed estimators have a bounded influence function and a redescending property so they are robust to outliers. The finite sample performance and property of the SLS estimators are studied and compared with other popular estimators in the literature through simulation studies and real world data examples.

The so-called 3σ-rule is a simple and widely used heuristic for outlier detection. This term is a generic term of some statistical hypothesis tests whose test statistics are known as normalized or studentized residuals. The conditions, under which this rule is statistically substantiated, were analyzed, and the extent it applies to geodetic least-squares adjustment was investigated. Then, the efficiency or non-efficiency of this method was analyzed and demonstrated on the example of repeated observations. / Die sogenannte 3σ-Regel ist eine einfache und weit verbreitete Heuristik für die Ausreißererkennung. Sie ist ein Oberbegriff für einige statistische Hypothesentests, deren Teststatistiken als normierte oder studentisierte Verbesserungen bezeichnet werden. Die Bedingungen, unter denen diese Regel statistisch begründet ist, werden analysiert. Es wird untersucht, inwieweit diese Regel auf geodätische Ausgleichungsprobleme anwendbar ist. Die Effizienz oder Nichteffizienz dieser Methode wird analysiert und demonstriert am Beispiel von Wiederholungsmessungen.

Ultra-wideband (UWB) technology is the next viable solution for applications in wireless personal area network (WPAN), body area network (BAN) and wireless sensor network (WSN). However, as application evolves toward a more realistic situation, wideband channel characteristics such as pulse distortion must be accounted for in channel modeling. Furthermore, application-oriented services such as ranging and localization demand fast prototyping, real-time processing of measured data, and good low signal-to-noise ratio (SNR) performance. Despite the tremendous effort being vested in devising new receivers by the global research community, channel-estimating Rake receiver is still one of the most promising receivers that can offer superior performance to the suboptimal counterparts. However, acquiring Nyquist-rate samples costs substantial power and resource consumption and is a major obstacle to the feasible implementation of the asymptotic maximum likelihood (ML) channel estimator. In this thesis, we address all three aspects of the UWB impulse radio (UWB-IR), in three separate contributions. First, we study the {\it a priori} dependency of the CLEAN deconvolution with real-world measurements, and propose a high-resolution, multi-template deconvolution algorithm to enhance the channel estimation accuracy. This algorithm is shown to supersede its predecessors in terms of accuracy, energy capture and computational speed. Secondly, we propose a {\it regularized} least squares time-of-arrival (ToA) estimator with wavelet denoising to the problem of ranging and localization with UWB-IR. We devise a threshold selection framework based on the Neyman-Pearson (NP) criterion, and show the robustness of our algorithm by comparing with other ToA algorithms in both computer simulation and ranging measurements when advanced digital signal processing (DSP) is available. Finally, we propose a low-complexity ML (LC-ML) channel estimator to fully exploit the multipath diversity with Rake receiver with sub-Nyquist rate sampling. We derive the Cram\'er-Rao Lower Bound (CRLB) for the LC-ML, and perform simulation to compare our estimator with both the $\ell_1$-norm minimization technique and the conventional ML estimator.

This thesis investigates several design problems concerning two-channel conjugate quadrature (CQ) filter banks and orthogonal wavelets, as well as orthogonal cosine-modulated (OCM) filter banks. It is well known that optimal design of CQ filters and wavelets and optimal design of prototype filters (PFs) of OCM filter banks in the least squares (LS) or minimax sense are nonconvex problems and to date only local solutions can be claimed. In this thesis, we first make some improvements over several direct design techniques for local design problems in terms of convergence and solution accuracy. By virtue of the recent progress in global polynomial optimization and the improved local design methods mentioned above, we describe an attempt at developing several design strategies that may be viewed as our endeavors towards global solutions for LS CQ filter banks, minimax CQ filter banks, and OCM filter banks. In brief terms, the proposed design strategies are based on several observations made among globally optimal impulse responses of low-order filter banks, and are essentially order-recursive algorithms in terms of filter length combined with some techniques in identifying a desirable initial point in each round of iteration. This main idea is applied to three design scenarios in this thesis, namely, LS design of orthogonal filter banks and wavelets, minimax design of orthogonal filter banks and wavelets, and design of orthogonal cosine-modulated filter banks. Simulation studies are presented to evaluate and compare the performance of the proposed design methods with several well established algorithms in the literature.