Extremal properties of certain risk models

Cette thèse s'intéresse à étudier les propriétés extrémales de certains modèles de risque d'intérêt dans diverses applications de l'assurance, de la finance et des statistiques. Cette thèse se développe selon deux axes principaux, à savoir: Dans la première partie, nous nous concentrons sur deux modèles de risques univariés, c'est-à- dire, un modèle de risque de déflation et un modèle de risque de réassurance. Nous étudions le développement des queues de distribution sous certaines conditions des risques commun¬s. Les principaux résultats sont ainsi illustrés par des exemples typiques et des simulations numériques. Enfin, les résultats sont appliqués aux domaines des assurances, par exemple, les approximations de Value-at-Risk, d'espérance conditionnelle unilatérale etc. La deuxième partie de cette thèse est consacrée à trois modèles à deux variables: Le premier modèle concerne la censure à deux variables des événements extrême. Pour ce modèle, nous proposons tout d'abord une classe d'estimateurs pour les coefficients de dépendance et la probabilité des queues de distributions. Ces estimateurs sont flexibles en raison d'un paramètre de réglage. Leurs distributions asymptotiques sont obtenues sous certaines condi¬tions lentes bivariées de second ordre. Ensuite, nous donnons quelques exemples et présentons une petite étude de simulations de Monte Carlo, suivie par une application sur un ensemble de données réelles d'assurance. L'objectif de notre deuxième modèle de risque à deux variables est l'étude de coefficients de dépendance des queues de distributions obliques et asymétriques à deux variables. Ces distri¬butions obliques et asymétriques sont largement utiles dans les applications statistiques. Elles sont générées principalement par le mélange moyenne-variance de lois normales et le mélange de lois normales asymétriques d'échelles, qui distinguent la structure de dépendance de queue comme indiqué par nos principaux résultats. Le troisième modèle de risque à deux variables concerne le rapprochement des maxima de séries triangulaires elliptiques obliques. Les résultats théoriques sont fondés sur certaines hypothèses concernant le périmètre aléatoire sous-jacent des queues de distributions. -- This thesis aims to investigate the extremal properties of certain risk models of interest in vari¬ous applications from insurance, finance and statistics. This thesis develops along two principal lines, namely: In the first part, we focus on two univariate risk models, i.e., deflated risk and reinsurance risk models. Therein we investigate their tail expansions under certain tail conditions of the common risks. Our main results are illustrated by some typical examples and numerical simu¬lations as well. Finally, the findings are formulated into some applications in insurance fields, for instance, the approximations of Value-at-Risk, conditional tail expectations etc. The second part of this thesis is devoted to the following three bivariate models: The first model is concerned with bivariate censoring of extreme events. For this model, we first propose a class of estimators for both tail dependence coefficient and tail probability. These estimators are flexible due to a tuning parameter and their asymptotic distributions are obtained under some second order bivariate slowly varying conditions of the model. Then, we give some examples and present a small Monte Carlo simulation study followed by an application on a real-data set from insurance. The objective of our second bivariate risk model is the investigation of tail dependence coefficient of bivariate skew slash distributions. Such skew slash distributions are extensively useful in statistical applications and they are generated mainly by normal mean-variance mixture and scaled skew-normal mixture, which distinguish the tail dependence structure as shown by our principle results. The third bivariate risk model is concerned with the approximation of the component-wise maxima of skew elliptical triangular arrays. The theoretical results are based on certain tail assumptions on the underlying random radius.

Sexual dimorphism of the human mandible: demonstration by elliptical Fourier analysis.

A new quantitative approach of the mandibular sexual dimorphism, based on computer-aided image analysis and elliptical Fourier analysis of the mandibular outline in lateral view is presented. This method was applied to a series of 117 dentulous mandibles from 69 male and 48 female individuals native of Rhenish countries. Statistical discriminant analysis of the elliptical Fourier harmonics allowed the demonstration of a significant sexual dimorphism in 97.1% of males and 91.7% of females, i.e. in a higher proportion than in previous studies using classical metrical approaches. This original method opens interesting perspectives for increasing the accuracy of sex identification in current anthropological practice and in forensic procedures.

Animal model to compare the effects of suture technique on cross-sectional compliance on end-to-side anastomoses.

OBJECTIVE: An animal model has been developed to compare the effects of suture technique on the luminal dimensions and compliance of end-to-side vascular anastomoses. METHODS: Carotid and internal mammalian arteries (IMAs) were exposed in three pigs (90 kg). IMAs were sectioned distally to perform end-to-side anastomoses on carotid arteries. One anastomosis was performed with 7/0 polypropylene running suture. The other was performed with the automated suture delivery device (Perclose/Abbott Labs Inc.) that makes a 7/0 polypropylene interrupted suture. Four piezoelectric crystals were sutured on toe, heel and both lateral sides of each anastomosis to measure anastomotic axes. Anastomotic cross-sectional area (CSAA) was calculated with: CSAA = pi x mM/4 where m and M are the minor and major axes of the elliptical anastomosis. Cross-sectional anastomotic compliance (CSAC) was calculated as CSAC=Delta CSAA/Delta P where Delta P is the mean pulse pressure and Delta CSAA is the mean CSAA during cardiac cycle. RESULTS: We collected a total of 1200000 pressure-length data per animal. For running suture we had a mean systolic CSAA of 26.94+/-0.4 mm(2) and a mean CSAA in diastole of 26.30+/-0.5 mm(2) (mean Delta CSAA was 0.64 mm(2)). CSAC for running suture was 4.5 x 10(-6)m(2)/kPa. For interrupted suture we had a mean CSAA in systole of 21.98+/-0.2 mm(2) and a mean CSAA in diastole of 17.38+/-0.3 mm(2) (mean Delta CSAA was 4.6+/-0.1 mm(2)). CSAC for interrupted suture was 11 x 10(-6) m(2)/kPa. CONCLUSIONS: This model, even with some limitations, can be a reliable source of information improving the outcome of vascular anastomoses. The study demonstrates that suture technique has a substantial effect on cross-sectional anastomotic compliance of end-to-side anastomoses. Interrupted suture may maximise the anastomotic lumen and provides a considerably higher CSAC than continuous suture, that reduces flow turbulence, shear stress and intimal hyperplasia. The Heartflo anastomosis device is a reliable instrument that facilitates performance of interrupted suture anastomoses.

Statistical Modeling of the Eye for Multimodal Treatment Planning for External Beam Radiation Therapy of Intraocular Tumors.

PURPOSE: Ocular anatomy and radiation-associated toxicities provide unique challenges for external beam radiation therapy. For treatment planning, precise modeling of organs at risk and tumor volume are crucial. Development of a precise eye model and automatic adaptation of this model to patients' anatomy remain problematic because of organ shape variability. This work introduces the application of a 3-dimensional (3D) statistical shape model as a novel method for precise eye modeling for external beam radiation therapy of intraocular tumors. METHODS AND MATERIALS: Manual and automatic segmentations were compared for 17 patients, based on head computed tomography (CT) volume scans. A 3D statistical shape model of the cornea, lens, and sclera as well as of the optic disc position was developed. Furthermore, an active shape model was built to enable automatic fitting of the eye model to CT slice stacks. Cross-validation was performed based on leave-one-out tests for all training shapes by measuring dice coefficients and mean segmentation errors between automatic segmentation and manual segmentation by an expert. RESULTS: Cross-validation revealed a dice similarity of 95% ± 2% for the sclera and cornea and 91% ± 2% for the lens. Overall, mean segmentation error was found to be 0.3 ± 0.1 mm. Average segmentation time was 14 ± 2 s on a standard personal computer. CONCLUSIONS: Our results show that the solution presented outperforms state-of-the-art methods in terms of accuracy, reliability, and robustness. Moreover, the eye model shape as well as its variability is learned from a training set rather than by making shape assumptions (eg, as with the spherical or elliptical model). Therefore, the model appears to be capable of modeling nonspherically and nonelliptically shaped eyes.

Value of positron emission tomography in full-thickness chest wall resections for malignancies.

Preoperative imaging for resection of chest wall malignancies is generally performed by computed tomography (CT). We evaluated the role of (18)F-fluorodeoxyglucose (FDG) positron emission tomography (PET) in planning full-thickness chest wall resections for malignancies. We retrospectively included 18 consecutive patients operated from 2004 to 2006 at our institution. Tumor extent was measured by CT and PET, using the two largest perpendicular tumor extensions in the chest wall plane to compute the tumor surface assuming an elliptical shape. Imaging measurements were compared to histopathology assessment of tumor borders. CT assessment consistently overestimated the tumor size as compared to PET (+64% vs. +1%, P<0.001). Moreover, PET was significantly better than CT at defining the size of lesions >24 cm(2) corresponding to a mean diameter >5.5 cm or an ellipse of >4 cm x 7.6 cm (positive predictive value 80% vs. 44% and specificity 93% vs. 64%, respectively). Metabolic PET imaging was superior to CT for defining the extent of chest wall tumors, particularly for tumors with a diameter >5.5 cm. PET can complement CT in planning full-thickness chest wall resection for malignancies, but its true value remains to be determined in larger, prospective studies.

A two-phase composite in simple shear: Effective mechanical anisotropy development and localization potential

We present a combined shape and mechanical anisotropy evolution model for a two-phase inclusion-bearing rock subject to large deformation. A single elliptical inclusion embedded in a homogeneous but anisotropic matrix is used to represent a simplified shape evolution enforced on all inclusions. The mechanical anisotropy develops due to the alignment of elongated inclusions. The effective anisotropy is quantified using the differential effective medium (DEM) approach. The model can be run for any deformation path and an arbitrary viscosity ratio between the inclusion and host phase. We focus on the case of simple shear and weak inclusions. The shape evolution of the representative inclusion is largely insensitive to the anisotropy development and to parameter variations in the studied range. An initial hardening stage is observed up to a shear strain of gamma = 1 irrespective of the inclusion fraction. The hardening is followed by a softening stage related to the developing anisotropy and its progressive rotation toward the shear direction. The traction needed to maintain a constant shear rate exhibits a fivefold drop at gamma = 5 in the limiting case of an inviscid inclusion. Numerical simulations show that our analytical model provides a good approximation to the actual evolution of a two-phase inclusion-host composite. However, the inclusions develop complex sigmoidal shapes resulting in the formation of an S-C fabric. We attribute the observed drop in the effective normal viscosity to this structural development. We study the localization potential in a rock column bearing varying fraction of inclusions. In the inviscid inclusion case, a strain jump from gamma = 3 to gamma = 100 is observed for a change of the inclusion fraction from 20% to 33%.

Comparison of accelerated T1-weighted whole-brain structural-imaging protocols.

Imaging in neuroscience, clinical research and pharmaceutical trials often employs the 3D magnetisation-prepared rapid gradient-echo (MPRAGE) sequence to obtain structural T1-weighted images with high spatial resolution of the human brain. Typical research and clinical routine MPRAGE protocols with ~1mm isotropic resolution require data acquisition time in the range of 5-10min and often use only moderate two-fold acceleration factor for parallel imaging. Recent advances in MRI hardware and acquisition methodology promise improved leverage of the MR signal and more benign artefact properties in particular when employing increased acceleration factors in clinical routine and research. In this study, we examined four variants of a four-fold-accelerated MPRAGE protocol (2D-GRAPPA, CAIPIRINHA, CAIPIRINHA elliptical, and segmented MPRAGE) and compared clinical readings, basic image quality metrics (SNR, CNR), and automated brain tissue segmentation for morphological assessments of brain structures. The results were benchmarked against a widely-used two-fold-accelerated 3T ADNI MPRAGE protocol that served as reference in this study. 22 healthy subjects (age=20-44yrs.) were imaged with all MPRAGE variants in a single session. An experienced reader rated all images of clinically useful image quality. CAIPIRINHA MPRAGE scans were perceived on average to be of identical value for reading as the reference ADNI-2 protocol. SNR and CNR measurements exhibited the theoretically expected performance at the four-fold acceleration. The results of this study demonstrate that the four-fold accelerated protocols introduce systematic biases in the segmentation results of some brain structures compared to the reference ADNI-2 protocol. Furthermore, results suggest that the increased noise levels in the accelerated protocols play an important role in introducing these biases, at least under the present study conditions.