In this dissertation, we investigate four distinct and interrelated problems for high-dimensional inference of mean vectors in multi-groups. The first problem concerned is the profile analysis of high dimensional repeated measures. We introduce new test statistics and derive its asymptotic distribution under normality for equal as well as unequal covariance cases. Our derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. We also derive consistent and unbiased estimators of the asymptotic variances for equal and unequal covariance cases respectively. The second problem considered is the accurate inference for high-dimensional repeated measures in factorial designs as well as any comparisons among the cell means. We derive asymptotic expansion for the null distributions and the quantiles of a suitable test statistic under normality. We also derive the estimator of parameters contained in the approximate distribution with second-order consistency. The most important contribution is high accuracy of the methods, in the sense that p-values are accurate up to the second order in sample size as well as in dimension. The third problem pertains to the high-dimensional inference under non-normality. We relax the commonly imposed dependence conditions which has become a standard assumption in high dimensional inference. With the relaxed conditions, the scope of applicability of the results broadens. The fourth problem investigated pertains to a fully nonparametric rank-based comparison of high-dimensional populations. To develop the theory in this context, we prove a novel result for studying the asymptotic behavior of quadratic forms in ranks. The simulation studies provide evidence that our methods perform reasonably well in the high-dimensional situation. Real data from Electroencephalograph (EEG) study of alcoholic and control subjects is analyzed to illustrate the application of the results.

En raison de la grande disponibilité de nouveaux types de caméras capturant des informations géométriques supplémentaires, ainsi que de l'émergence de nouvelles modalités d'image telles que les champs de lumière et les images omnidirectionnelles, il est nécessaire de stocker et de diffuser une quantité énorme de hautes dimensions. Les exigences croissantes en matière de streaming et de stockage de ces nouvelles modalités d’image nécessitent de nouveaux outils de codage d’images exploitant la structure complexe de ces données. Cette thèse a pour but d'explorer de nouvelles approches basées sur les graphes pour adapter les techniques de codage de transformées d'image aux types de données émergents où les informations échantillonnées reposent sur des structures irrégulières. Dans une première contribution, de nouvelles transformées basées sur des graphes locaux sont conçues pour des représentations compactes des champs de lumière. En tirant parti d’une conception minutieuse des supports de transformées locaux et d’une procédure d’optimisation locale des fonctions de base , il est possible d’améliorer considérablement le compaction d'énergie. Néanmoins, la localisation des supports ne permettait pas d'exploiter les dépendances à long terme du signal. Cela a conduit à une deuxième contribution où différentes stratégies d'échantillonnage sont étudiées. Couplés à de nouvelles méthodes de prédiction, ils ont conduit à des résultats très importants en ce qui concerne la compression quasi sans perte de champs de lumière statiques. La troisième partie de la thèse porte sur la définition de sous-graphes optimisés en distorsion de débit pour le codage de contenu omnidirectionnel. Si nous allons plus loin et donnons plus de liberté aux graphes que nous souhaitons utiliser, nous pouvons apprendre ou définir un modèle (ensemble de poids sur les arêtes) qui pourrait ne pas être entièrement fiable pour la conception de transformées. La dernière partie de la thèse est consacrée à l'analyse théorique de l'effet de l'incertitude sur l'efficacité des transformées basées graphes. / Due to the large availability of new camera types capturing extra geometrical information, as well as the emergence of new image modalities such as light fields and omni-directional images, a huge amount of high dimensional data has to be stored and delivered. The ever growing streaming and storage requirements of these new image modalities require novel image coding tools that exploit the complex structure of those data. This thesis aims at exploring novel graph based approaches for adapting traditional image transform coding techniques to the emerging data types where the sampled information are lying on irregular structures. In a first contribution, novel local graph based transforms are designed for light field compact representations. By leveraging a careful design of local transform supports and a local basis functions optimization procedure, significant improvements in terms of energy compaction can be obtained. Nevertheless, the locality of the supports did not permit to exploit long term dependencies of the signal. This led to a second contribution where different sampling strategies are investigated. Coupled with novel prediction methods, they led to very prominent results for quasi-lossless compression of light fields. The third part of the thesis focuses on the definition of rate-distortion optimized sub-graphs for the coding of omni-directional content. If we move further and give more degree of freedom to the graphs we wish to use, we can learn or define a model (set of weights on the edges) that might not be entirely reliable for transform design. The last part of the thesis is dedicated to theoretically analyze the effect of the uncertainty on the efficiency of the graph transforms.

<p>Contrast-enhanced magnetic resonance angiography (MRA) is used to obtain images showing the vascular system. To detect stenosis, which is narrowing of for example blood vessels, maximum intensity projection (MIP) is typically used. This technique often fails to demonstrate the stenosis if the projection angle is not suitably chosen. To improve identification of this region a color-coding algorithm could be helpful. The color should be carefully chosen depending on the vessel diameter. </p><p>In this thesis a segmentation to produce a binary 3d-volume is made, followed by a distance transform to approximate the Euclidean distance from the centerline of the vessel to the background. The distance is used to calculate the smallest diameter of the vessel and that value is mapped to a color. This way the color information regarding the diameter would be the same from all the projection angles. </p><p>Color-coded MIPs, where the color represents the maximum distance, are also implemented. The MIP will result in images with contradictory information depending on the angle choice. Looking in one angle you would see the actual stenosis and looking in another you would see a color representing the abnormal diameter.</p>

A valuable analytical tool to understand the event of ruin is a Gerber-Shiu discounted penalty function. It acts as a unified means of identifying ruin-related quantities which may help insurers understand their vulnerability ruin. This thesis provides an introduction to the basic concepts and common techniques used for the Gerber-Shiu analysis. Chapter 1 introduces the insurer's surplus process in the ordinary Sparre Andersen model. Defective renewal equations, the Dickson-Hipp transform, and Lundberg's fundamental equation are reviewed. Chapter 2 introduces the classical Gerber-Shiu discounted penalty function. Two framework equations are derived by conditioning on the first drop in surplus below its initial value, and by conditioning on the time and amount of the first claim. A detailed discussion is provided for each of these conditioning arguments. The classical Poisson model (where interclaim times are exponentially distributed) is then considered. We also consider when claim sizes are exponentially distributed. Chapter 3 introduces the Gerber-Shiu function in the delayed renewal model which allows the time until the first claim to be distributed differently than subsequent interclaim times. We determine a functional relationship between the Gerber-Shiu function in the ordinary Sparre Andersen model and the Gerber-Shiu function in the delayed model for a class of first interclaim time densities which includes the equilibrium density for the stationary renewal model, and the exponential density. To conclude, Chapter 4 introduces a generalized Gerber-Shiu function where the penalty function includes two additional random variables: the minimum surplus level before ruin, and the surplus immediately after the claim before the claim causing ruin. This generalized Gerber-Shiu function allows for the study of random variables which otherwise could not be studied using the classical definition of the function. Additionally, it is assumed that the size of a claim is dependant on the interclaim time that precedes it. As is done in Chapter 2, a detailed discussion of each of the two conditioning arguments is provided. Using the uniqueness property of Laplace transforms, the form of joint defective discounted densities of interest are determined. The classical Poisson model and the exponential claim size assumption is also revisited.

Wavelet methods for image denoising have became widespread for the last decade. The effectiveness of this denoising scheme is influenced by many factors. Highlights can be listed as choosing of wavelet used, the threshold determination and transform level selection for thresholding. For threshold calculation one of the classical solutions is Wiener filter as a linear estimator. Another one is VisuShrink using global thresholding for nonlinear area. The purpose of this work is to develop a Java toolbox which is used to find best denoising schemes for distinct image types particularly Synthetic Aperture Radar (SAR) images. This can be accomplished by comparing these basic methods with well known data adaptive thresholding methods such as SureShrink, BayeShrink, Generalized Cross Validation and Hypothesis Testing. Some nonwavelet denoising process are also introduced. Along with simple mean and median filters, more statistically adaptive median, Lee, Kuan and Frost filtering techniques are also tested to assist wavelet based denoising scheme. All of these methods on the basis of wavelet models and some traditional methods will be implemented in pure java code using plug-in concept of ImageJ which is a popular image processing tool written in Java.

In this thesis a stepped-frequency Inverse Synthetic Aperture Radar (ISAR) is employed to develop two-dimensional range-Doppler images of a small ghter aircraft which exhibits three dimensional rotational rotation. The simulation is designed such that the target can exhibit yaw, pitch and roll motions at the same time. First, radar returns from prominent scatterers of various parts of the target are processed and displayed using conventional Fourier transform. The eects of dierent complex motion types and scenarios are observed and discussed. Then, several linear and bi-linear time-frequency distributions including shorttime Fourier transform, Wigner-Ville, pseudo Wigner-Ville, smoothed pseudo Wigner-Ville, Choi-Williams, Born-Jordan and Zhao-Atlas-Marks distributions are applied to the same target and scenarios. The performance of the transforms is compared for each scenario. The reasons for success of the distributions are discussed thoroughly.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 136-138). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 136-138). Also available on the Internet.

Thesis (Ph. D.)--York University, 2001. Graduate Programme in Computer Science. / Typescript. Includes bibliographical references (leaves 132-142). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ66340

Darbe gaunama, jog silpno matų konvergavimo erdvės X prasme išlpaukia charakteringųjų transformacijų konvergavimas ir atvirkščiai, jeigu charakteringosios transformacijos konverguoja į funkcijas tolydžias nuliniame taške, tai iš čia išplaukia matų silpnas konvergavimas erdvės X prasme. / It is obtained, that the weak convergence in the sense of X implies the convergence of characteristic transforms, and, on the contrary, if the characteristic transforms converge weakly to the functions contiuous at zero, the from this the weak convergence in the sense of X for the probability measures fallows.