It is of great importance to find an analytical copula that will represent the empirical lower tail dependence. In this study, the pairwise empirical copula are estimated using data of the S&P 500 stocks during the period 2007-2010.Different optimization methods and measures of dependence have been used to fit Gaussian, t and Clayton copula to the empirical copulas, in order to represent the empirical lower tail dependence. These different measures of dependence and optimization methods with their restrictions, point at different analytical copulas being optimal. In this study the t copula with 5 degrees of freedom is giving the most fulfilling result, when it comes to representing lower tail dependence. The t copula with 5 degrees of freedom gives the best representation of empirical lower tail dependence, whether one uses the 'Empirical maximum likelihood estimator', or 'Equal Ƭ' as an approach.

Il est bien connu que les lois marginales d'un vecteur aléatoire ne susent pas à caractériser sa distribution. Lorsque les lois marginales du vecteur aléatoire sont continues, le théorème de Sklar garantit l'existence et l'unicité d'une fonction appelée copule, caractérisant la dépendance entre les composantes du vecteur. La loi du vecteur aléatoire est parfaitement dénie par la donnée des lois marginales et de la copule. Dans ce travail de thèse, nous proposons deux tests non paramétriques de détection de ruptures dans la distribution d'observations multivariées, particulièrement sensibles à des changements dans la copule des observations. Ils améliorent tous deux des propositions récentes et donnent lieu à des tests plus puissants que leurs prédécesseurs pour des classes d'alternatives pertinentes. Des simulations de Monte Carlo illustrent les performances de ces tests sur des échantillons de taille modérée. Le premier test est fondé sur une statistique à la Cramér-von Mises construite à partir du processus de copule empirique séquentiel. Une procédure de rééchantillonnage à base de multiplicateurs est proposée pour la statistique de test ; sa validité asymptotique sous l'hypothèse nulle est démontrée sous des conditions de mélange fort sur les données. Le second test se focalise sur la détection d'un changement dans le rho de Spearman multivarié des observations. Bien que moins général, il présente de meilleurs résultats en terme de puissance que le premier test pour les alternatives caractérisées par un changement dans le rho de Spearman. Deux stratégies de calcul de la valeur p sont comparées théoriquement et empiriquement : l'une utilise un rééchantillonnage de la statistique, l'autre est fondée sur une estimation de la loi limite de la statistique de test. / It is very well-known that the marginal distributions of a random vector do not characterize the distribution of the random vector. When the marginal distributions are continuous, the work of Sklar ensures the existence and uniqueness of a function called copula which can be regarded as capturing the dependence between the components of the random vector. The cumulative distribution function of the vector can then be rewritten using only the copula and the marginal cumulative distribution functions. In this work, we propose two non-parametric tests for change-point detection, particularly sensitive to changes in the copula of multivariate time series. They improve on recent propositions and are more powerful for relevant alternatives involving a change in the copula. The finite-sample behavior of these tests is investigated through Monte Carlo experiments. The first test is based on a Cramér-von Mises statistic and on the sequential empirical copula process. A multiplier resampling scheme is suggested and its asymptotic validity under the null hypothesis is demonstrated under strong mixing conditions. The second test focuses on the detection of a change in Spearman's rho. Monte Carlo simulations reveal that this test is more powerful than the first test for alternatives characterized by a change in Spearman's rho. Two approaches to compute approximate p-values for the test are studied empirically and theoretically. The first one is based on resampling, the second one consists of estimating the asymptotic null distribution of the test statictic.

This research study examines the manner in which a cardiological sample presents in terms of their psychological make-up by making specific reference to the constructs self-concept and emotions. A literature overview of different aspects of self-concept, emotion and cardiology places the results and discussions of the study within a theoretical background. The study supplies descriptive information relating to the demographic profile of the sample, followed by a description of various aspects of self-concept and emotions, as well as a correlational exploration of the manner in which the sample group presents. The sample consisted of 29 individuals, all who had been diagnosed with coronary heart disease (CHD) and been subjected to surgery as a result thereof. The participants completed a questionnaire, containing two measurement instruments, namely the Adolescent Self-Concept Scale (ASCS) and the Emotions Profile Index (EPI). The scores, obtained by the sample, were subjected to statistical analysis to provide a self-conceptual and emotional profile of the sample. The Spearman Rank-Order Correlation Coefficient was then used to indicate the extent to which the sample tended towards portraying themselves in a positive light, more than they might be experiencing. The study further refers to the views of the sample group, relating to these findings, as obtained from an information and discussion session held with them. The study indicate a significant statistical trend amongst the sample group to portray themselves in a positive light in relation to emotions, even though they were not in reality experiencing such positive emotions. Although the same positive trend was indicated with self-concept, the study cannot conclusively indicate that this is not a realistic presentation of the sample group as a whole. / Dissertation (Counselling Psychology)--University of Pretoria, 2006. / Psychology / unrestricted

The work occupy by inverse analysis based on artificial neural network. This identification algorithm enable correct determine parameters of applied material model on creation of numerical model of construction so it's possible that the results of computerized simulation correspond with experiments. It look's like suitable approach especially in cases with complicated problems and complex models with many material parameters.