Cette thèse a pour objectif d’améliorer la détection de cibles lentes et de faible réflectivité dans le cas de radars de sol Doppler pulsés à fréquence de récurrence intermédiaire. Ces radars, hautement ambigus en distance et en vitesse, émettent de façon consécutive des trains d’impulsions de périodes de récurrence différentes, afin de lever les ambiguïtés.L’émission successive de trains d’impulsions de courtes durées conduit à une faible capacité de séparation sur l’axe Doppler. Par conséquent, les objets lents de faible réflectivité, comme les drones, sont difficiles à distinguer du fouillis de sol. A l’issue du traitement Doppler conventionnel qui vise à éliminer les échos de fouillis, les performances de détection de ces cibles sont fortement atténuées. Pour palier à ce problème, nous avons développé une nouvelle chaîne de traitement 2D distance/Doppler pour les radars à fréquence de récurrence intermédiaire. Celle-ci s’appuie, en premier lieu, sur un algorithme itératif permettant d’exploiter la diversité temporelle entre les trains d’impulsions émis, afin de lever les ambiguïtés en distance et en vitesse et de détecter les cibles rapides exo-fouillis. La détection des cibles lentes endo-fouillis est ensuite réalisée à l’aide d’un détecteur adaptatif. Une nouvelle approche, permettant d’associer les signaux issus de rafales de caractéristiques différentes pour l’estimation de la matrice de covariance, est utilisée en vue d’optimiser les performances de détection. Les différents tests effectués sur données simulées et réelles pour évaluer les traitements développés et la nouvelle chaîne de traitement, ont montré l’intérêt de ces derniers. / The aim of this thesis is to enhance the detection of slow-moving targets with low reflectivity in case of ground-based pulse Doppler radars operating in intermediate pulse repetition frequency. These radars are highly ambiguous in range and Doppler. To resolve ambiguities, they transmit successively short pulse trains with different pulse repetition intervals. The transmission of short pulse trains results in a poor Doppler resolution. As consequence, slow-moving targets with low reflectivity, such as unmanned aerial vehicles, are buried into clutter returns. One of the main drawbacks of the classical Doppler processing of intermediate pulse repetition frequency pulse Doppler radars is the low detection performance of small and slowly-moving targets after ground clutter rejection. In order to address this problem, a two-dimensional range / Dopper processing chain including new techniques is proposed in this thesis. First, an iterative algorithm allows to exploit transmitted pulse trains temporal diversity to resolve range and Doppler ambiguities and detect fast, exo-clutter, targets. The detection of slow, endo-clutter, targets is then performed by an adaptive detection scheme. It uses a new covariance matrix estimation approach allowing the association of pulse trains with different characteristics in order to enhance detection performance. The different tests performed on simulated and real data to evaluate the proposed techniques and the new processing chain have shown their effectiveness.

Dans cette thèse nous nous intéressons au modèle linéaire général (modèle linéaire multivarié) en grande dimension. Nous proposons un nouvel estimateur parcimonieux des coefficients de ce modèle qui prend en compte la dépendance qui peut exister entre les différentes réponses. Cet estimateur est obtenu en estimant dans un premier temps la matrice de covariance des réponses puis en incluant cette matrice de covariance dans un critère Lasso. Les propriétés théoriques de cet estimateur sont étudiées lorsque le nombre de réponses peut tendre vers l’infini plus vite que la taille de l’échantillon. Plus précisément, nous proposons des conditions générales que doivent satisfaire les estimateurs de la matrice de covariance et de son inverse pour obtenir la consistance en signe des coefficients. Nous avons ensuite mis en place des méthodes, adaptées à la grande dimension, pour l’estimation de matrices de covariance qui sont supposées être des matrices de Toeplitz ou des matrices avec une structure par blocs, pas nécessairement diagonaux. Ces différentes méthodes ont enfin été appliquées à des problématiques de métabolomique, de protéomique et d’immunologie. / In this PhD thesis we study general linear model (multivariate linearmodel) in high dimensional settings. We propose a novel variable selection approach in the framework of multivariate linear models taking into account the dependence that may exist between the responses. It consists in estimating beforehand the covariance matrix of the responses and to plug this estimator in a Lasso criterion, in order to obtain a sparse estimator of the coefficient matrix. The properties of our approach are investigated both from a theoretical and a numerical point of view. More precisely, we give general conditions that the estimators of the covariance matrix and its inverse have to satisfy in order to recover the positions of the zero and non-zero entries of the coefficient matrix when the number of responses is not fixed and can tend to infinity. We also propose novel, efficient and fully data-driven approaches for estimating Toeplitz and large block structured sparse covariance matrices in the case where the number of variables is much larger than the number of samples without limiting ourselves to block diagonal matrices. These approaches are appliedto different biological issues in metabolomics, in proteomics and in immunology.

Testing the equality between two high-dimensional covariance matrices is challenging. As the most efficient way to measure evidential discrepancies in observed data, the likelihood ratio test is expected to be powerful when the null hypothesis is violated. However, when the data dimensionality becomes large and potentially exceeds the sample size by a substantial margin, likelihood ratio based approaches face practical and theoretical challenges. To solve this problem, this study proposes a method by which we first randomly project the original high-dimensional data into lower-dimensional space, and then apply the corrected likelihood ratio tests developed with random matrix theory. We show that testing with a single random projection is consistent under the null hypothesis. Through evaluating the power function, which is challenging in this context, we provide evidence that the test with a single random projection based on a random projection matrix with reasonable column sizes is more powerful when the two covariance matrices are unequal but component-wise discrepancy could be small -- a weak and dense signal setting. To more efficiently utilize this data information, we propose combined tests from multiple random projections from the class of meta-analyses. We establish the foundation of the combined tests from our theoretical analysis that the p-values from multiple random projections are asymptotically independent in the high-dimensional covariance matrices testing problem. Then, we show that combined tests from multiple random projections are consistent under the null hypothesis. In addition, our theory presents the merit of certain meta-analysis approaches over testing with a single random projection. Numerical evaluation of the power function of the combined tests from multiple random projections is also provided based on numerical evaluation of power function of testing with a single random projection. Extensive simulations and two real genetic data analyses confirm the merits and potential applications of our test. / Statistics

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This paper explores different covariance matrix estimators in application to geometric Brownian motion. Particular interest is given to shrinkage estimation methods. In collaboration with Söderberg & Partners risk management team, the goal is to find an estimation that performs well in low-data scenarios and is robust against erroneous model assumptions, particularly the Gaussian assumption of the stock price distribution. Estimations are compared by two criteria: Frobenius norm distance between the estimate and the true covariance matrix, and the condition number of the estimate. By considering four estimates — the sample covariance matrix, Ledoit-Wolf, Tyler M-estimator, and a novel Tyler-Ledoit-Wolf (TLW) estimator — this paper concludes that the TLW estimator performs best when considering the two criteria.

Dentro da biologia evolutiva, uma das questões centrais é a compreensão de como os processos evolutivos, em particular a seleção e o acaso (deriva genética) moldaram a diversidade obervada nos organismos. Dentro deste contexto, a utilização de abordagens como a integração morfológica e a genética quantitativa nos fornecem poderosas ferramentas. Enquanto a primeira descreve os padrões de relação entre caracteres e testa hipóteses sobre as relações de desenvolvimento e/ou funções subjacentes, a segunda possui ferramentas para investigar as forças que podem ter gerado os fenótipos atuais. Utilizando como modelo de estudo os gêneros de marsupiais da Ordem Didelphimorphia, analisei a evolução morfológica craniana unindo estas duas linhas de pesquisa. Central a genética quantitativa está a matriz de covariância genética (G) que descreve a porção da variância que é efetivamente herdada (no sentido de transmissão de valor entre gerações) e conseqüentemente serve como substrato à seleção. Apesar de ter sido desenvolvida inicialmente para estudos em escala microevolutiva, o arsenal matemático da genética quantitativa pode ser estendida a escalas macroevolutivas caso a matriz G permaneça relativamente estável. Entretanto, como a estimativa de uma matriz G requer um número grande de espécimes aparentados e com genealogia conhecida, utilizei ao longo deste trabalho sua correspondente fenotípica (P). Desta forma, no primeiro capítulo demonstrei a similaridade das matrizes de covariância e correlação P dos marsupiais Didelphimorphia. Em contrapartida, as magnitudes de integração morfológica, que medem o grau de associação entre os caracteres, se mostraram mais variáveis dentro do grupo. A história evolutiva (filogenia) e as distâncias morfológicas entre os gêneros não parecem ter tido influência sobre os padrões nem as magnitudes, já que não se correlacionaram significativamente a eles. No segundo capítulo, estendi estas análises para os gêneros ao longo do seu desenvolvimento e novamente os padrões se mostraram semelhantes, tanto quando comparei a ontogenia de um único gênero, quando analisei diferentes gêneros para diferentes classes etárias. Em contrapartida, as magnitudes de integração se mostraram mais variáveis, com uma tendência a diminuírem com o aumento da idade. Por conta destes resultados, comparei as matrizes de correlação empíricas com matrizes teóricas que expressam hipóteses de modularidade baseadas no desenvolvimento/função compartilhada pelas regiões do crânio. Testei para similaridade das duas regiões principais (face e neurocrânio), cinco sub-regiões (base e abóboda craniana, oral, nasal e zigomático), uma matriz 198 de integração somática (caracteres neurais vs. faciais) e uma de integração total, concatenando as cinco sub-regiões. Foram encontradas somente correlações significativas para as regiões da face e suas sub-regiões nasal e oral. Apesar das variações nas magnitudes de integração observadas nestes dois primeiros capítulos, as respostas evolutivas obtidas para estes gêneros foram todas muito similares. Este resultado, associado a constatação de que grande parte da variação entre os espécimes é devida ao tamanho, ou variações de forma associadas a ele (alometria), me levaram a analisar as conseqüências evolutivas associadas a estas variações alométricas. Assim, no terceiro capítulo analisei as direções de resposta à seleção simulada antes e após a remoção do tamanho. Variações alométricas exercem forte influência sobre estes crânios tornando-os muito integrados morfologicamente, ou seja, a percepção dos módulos que os compõem é muito difícil (baixa modularidade). Isto se reflete em uma maior variação ao longo da linha de menor resistência evolutiva (que resume o eixo de maior variação disponível entre os espécimes), já que os módulos não podem responder a seleção de forma independente (alta integração morfológica). Em marsupiais, esta linha é está alinhada na direção de variações de tamanho. Desta forma, não importa em que direção a seleção esteja atuando, as respostas evolutivas serão usualmente na direção desta linha de menor resistência e conseqüentemente de tamanho. Uma vez que o tamanho é removido, as magnitudes de integração diminuem e a modularidade do crânio aumenta. Por conseguinte, ele passa a ser capaz de responder à seleção em uma gama maior de direções porque aumenta também a relativa independência destes módulos em relação aos demais. Como estes resultados indicam que variações entre os Didelphimorphia são direcionadas a variações no tamanho, devido justamente às restrições impostas pela linha de menor resistência evolutiva, analisei as trajetórias ontegenéticas de dois gêneros irmãos, Didelphis e Philander, separando os efeitos da forma e tamanho nesta diversificação. Para tanto empreguei análises de morfometria tradicional, morfométrica e análises de coeficientes alométricos que apontaram para uma maior diferenciação no tamanho entre eles. Apesar da similaridade entre as trajetórias ontogenéticas destes dois gêneros, espécimes de Didelphis nascem maiores e crescem por mais tempo, como indicado pela sua trajetória mais longa. / One of the central goals in evolutionary biology is related to how evolutionary processes, mainly natural selection and genetic drift, shaped living organisms. The combined use of Morphologial Integration and Quantitative Genetics give us powerful tools to accomplish this goal. Morphological Integration is concerned of how characters are related, as well as their underlying genetics/developmental relationship, while Quantitative Genetics have methodologies designed to explore the phenotypic forces underlying diversity among organisms. Using Didelphimorphia marsupials as a study group, I combined these two approaches to study its morphologic cranial diversification. In Quantitative Genetics, the genetic additive covariance matrix (G) resume the genetic variation underlying resemblance among relatives, which is the portion of the variance responsive to selection. Initially developed to microevolutionary scale studies, it can be extended to a macroevolutionary scale if it remains relatively similar in that time scale. However, as G matrix estimations require a huge number of related specimens with known genealogy, I used its phenotypic (P) counterpart which was more easily obtained. In the first chapter I showed high similarities among Didelphimorphia marsupials covariance and correlation P matrices. On the other hand, integration magnitudes (which measure the average correlation among traits) vary among taxa. Neither phylogeny nor morphologic distances showed any association with the similarity in patterns and magnitudes of integration. In the second chapter, I did these same analyses, but throughout genera ontogeny. Again, there was a high similarity among taxa in patterns of integration, both when I analyzed the ontogeny for each genus separately or against each other (at different age class). Morphological integration magnitudes showed the same variation obtained for adults, with a tendency to decrease at older ages. Taking these results into account, I compared the phenotypic correlation matrices to theoretical matrices, based on hypotheses of shared developmental and functional units. I searched for modularity in the two main skull regions (face and neurocranium) and five sub regions (cranium base and vault, face, nasal, and oral). I also looked for modularity concerning somatic development (Neurocranium vs. Face) and total modularity, as the 200 summation of the five sub-regions. Only Face and its sub-regions nasal and oral, showed significant correlations to the phenotypic genera matrices. Despite integration magnitude differences, all evolutionary responses produced by taxa were highly similar. These results, combined with a huge size variation (or size related variation - allometry) across taxa, lead me to search for the evolutionary consequences due to size variation. In the third chapter, I compared evolutionary response directions produce by each genera matrices before and after size removal under a random selection simulation. Allometry strongly affect these skulls, turning them into highly integrated structures with lower modularity (skull modules are not easily distinguished). Because of this, modules cannot evolve relatively independent of other modules and evolutionary responses will strongly affect the whole cranium. This is related to the variation along the lines of least evolutionary resistance. This line is the multivariate direction of greatest genetic or phenotypic variation (the combination of a suite of traits that displays the maximum within-population variance). In Didelphimorphia marsupials, this line is aligned with size variation and regardless the selection direction, evolutionary change is usually aligned to this least resistance line. The removal of size variation diminish the magnitude of integration while increases modularity. Consequently, skulls become able to respond to selection in more directions as modules become relatively more independent of each other. In the last chapter I compared size and shape differences between ontogenetic trajectories of two sister genera Didelphis and Philander. Using traditional and geometric morphometric analysis plus allometric coefficient analysis, I could show that bigger differences between them are size related. Despite similarities, ontogenetic trajectory in Didelphis is longer, leading to bigger specimens.

Nesta dissertação, foi utilizada a técnica SIFT (Scale Invariant Feature Transform) para o reconhecimento de imagens da área dos olhos (região periorbital). Foi implementada uma classificação das imagens em subgrupos internos ao banco de dados, utilizando-se das informações estatísticas provenientes dos padrões invariantes produzidos pela técnica SIFT. Procedeu-se a uma busca categorizada pelo banco de dados, ao invés da procura de um determinado padrão apresentado, através da comparação deste com cada padrão presente no banco de dados. A tais padrões foi aplicada uma abordagem estatística, através da geração da matriz de covariâncias dos padrões gerados, sendo esta utilizada para a categorização, tendo por base uma rede neural híbrida. A rede neural classifica e categoriza o banco de dados de imagens, criando uma topologia de busca. Foram obtidos resultados corretos de classificação de 76,3% pela rede neural híbrida, sendo que um algoritmo auxiliar determina uma hierarquia de busca, onde, ocorrendo uma errônea classificação, a busca segue em grupos de pesquisas mais prováveis.

This thesis has treated the subject of DCC-GARCH model’s forecasting ability and Value-at- Risk applications on the Scandinavian foreign exchange market. The estimated models were based on daily opening foreign exchange spot rates in the period of 2004-2013, which captured the information in the financial crisis of 2008 and Eurozone crisis in the early 2010s. The forecasts were performed on a one-day rolling window in 2014. The results show that the DCC-GARCH model accurately predicted the fluctuation in the conditional correlation, although not with the correct magnitude. Furthermore, the DCC-GARCH model shows good Value-at-Risk forecasting performance for different portfolios containing the Scandinavian currencies.

<p>Two methods for evaluating and improving plane wave beamforming have beendeveloped. The methods estimate the shape of the wavefront and use theinformation in the beamforming. One of the methods uses estimates of the timedelays between the sensors to approximate the shape of the wavefront, and theother estimates the wavefront by matching the received wavefront to sphericalwavefronts of different radii. The methods are compared to a third more commonmethod of beamforming, which assumes that the impinging wave is planar. Themethods’ passive ranging abilities are also evaluated, and compared to a referencemethod based on triangulation.Both methods were evaluated with both real and simulated data. The simulateddata was obtained using Raylab, which is a simulation program based on ray-tracing. The real data was obtained through a field-test performed in the Balticsea using a towed array sonar and a stationary source emitted tones.The performance of the matched beamformers depends on the distance to the tar-get. At a distance of 600 m near broadside the power received by the beamformerincreases by 0.5-1 dB compared to the plane wave beamformer. At a distance of300 m near broadside the improvement is approximately 2 dB. In general, obtain-ing an accurate distance estimation proved to be difficult, and highly dependenton the noise present in the environment. A moving target at a distance of 600 mat broadside can be estimated with a maximum error of 150 m, when recursiveupdating of the covariance matrix with a updating constant of 0.25 is used. Whenrecursive updating is not used the margin of error increases to 400 m.</p>

This thesis deals with univariate and multivariate rank methods in making statistical inference. It is assumed that the underlying distributions belong to the class of elliptical distributions. The class of elliptical distributions is an extension of the normal distribution and includes distributions with both lighter and heavier tails than the normal distribution. In the first part of the thesis the rank covariance matrices defined via the Oja median are considered. The Oja rank covariance matrix has two important properties: it is affine equivariant and it is proportional to the inverse of the regular covariance matrix. We employ these two properties to study the problem of estimating the rank covariance matrices when they have a certain structure. The second part, which is the main part of the thesis, is devoted to rank estimation in linear regression models with symmetric heteroscedastic errors. We are interested in asymptotic properties of rank estimates. Asymptotic uniform linearity of a linear rank statistic in the case of heteroscedastic variables is proved. The asymptotic uniform linearity property enables to study asymptotic behaviour of rank regression estimates and rank tests. Existing results are generalized and it is shown that the Jaeckel estimate is consistent and asymptotically normally distributed also for heteroscedastic symmetric errors.