Characterizing drought using the reliability-resilience-vulnerability concept

This study borrows the measures developed for the operation of water resources systems as a means of characterizing droughts in a given region. It is argued that the common approach of assessing drought using a univariate measure (severity or reliability) is inadequate as decision makers need assessment of the other facets considered here. It is proposed that the joint distribution of reliability, resilience, and vulnerability (referred to as RRV in a reservoir operation context), assessed using soil moisture data over the study region, be used to characterize droughts. Use is made of copulas to quantify the joint distribution between these variables. As reliability and resilience vary in a nonlinear but almost deterministic way, the joint probability distribution of only resilience and vulnerability is modeled. Recognizing the negative association between the two variables, a Plackett copula is used to formulate the joint distribution. The developed drought index, referred to as the drought management index (DMI), is able to differentiate the drought proneness of a given area when compared to other areas. An assessment of the sensitivity of the DMI to the length of the data segments used in evaluation indicates relative stability is achieved if the data segments are 5years or longer. The proposed approach is illustrated with reference to the Malaprabha River basin in India, using four adjoining Climate Prediction Center grid cells of soil moisture data that cover an area of approximately 12,000 km(2). (C) 2013 American Society of Civil Engineers.

Comportamento territorial de Lipaugus lanioides (Aves: Cotingidae) em área de Floresta Atlântica na Ilha Grande, RJ

O comportamento territorial é uma estratégia de monopolização de recursos quando esses são essenciais para o sucesso reprodutivo de um organismo. Um território é uma área de uso exclusivo, defendido contra invasores coespecíficos de mesmo sexo, resultante da interação social entre vizinhos. A territorialidade exerce importante papel no sistema reprodutivo de uma espécie, pois influencia a participação do macho na reprodução. Nesses casos, as fêmeas podem obter vantagens diretas, como sítios de nidificação e cuidado parental. O comportamento territorial também exerce influência na regulação do tamanho populacional através de uma relação entre custos e benefícios individuais: em ambientes ótimos e com alta densidade populacional, os territórios são pequenos com pouca substituição, e jovens machos têm dificuldade para conseguirem estabelecer-se. O presente estudo teve como objetivo investigar aspectos comportamentais do tropeiro-da-serra, espécie rara e endêmica de Floresta Atlântica, com distribuição bastante restrita. Ao longo de 18 meses na Ilha Grande (RJ), analisamos seu comportamento territorial, mensuramos os tamanhos de territórios individuais de machos e realizamos estimativas de densidade populacional. O playback foi utilizado para atestar a presença de territorialidade na espécie, para simular a aproximação de coespecíficos (interações intraespecíficas) e para induzir o deslocamento dos indivíduos até os limites de seus territórios. Para investigar as respostas comportamentais à aproximação de invasores, analisamos quantitativamente as reações dos indivíduos a estímulos sonoros (vocalização espontânea e induzida pelo playback). Os territórios individuais foram definidos em duas estações reprodutivas através do método do Mínimo Polígono Convexo (MPC) em uma área equivalente a 20ha. A densidade populacional foi definida através do número de territórios encontrados e pelo número de indivíduos vistos/ouvidos por unidade de área através de transecções lineares. As vocalizações espontâneas e induzidas ocorreram somente entre os meses de agosto a janeiro, caracterizando uma estação reprodutiva bem definida. Durante este período, os machos tornaram-se solitários e agressivos com coespecíficos; na fase não-reprodutiva, entretanto, os indivíduos mostram-se sociáveis, forrageando em pequenos grupos de até quatro indivíduos. Os resultados indicam que o território é estabelecido para a monopolização de alimento e acesso às fêmeas. Essas observações sugerem que a espécie estudada é territorialista. Foram estimados sete territórios com valores entre 0,21ha e 0,73ha (0,43 + 0,16ha). Os indivíduos apresentaram fidelidade territorial, ocupando os mesmos territórios em duas estações reprodutivas. A densidade populacional de L. lanioides apresentou flutuações ao longo do ano, com os maiores valores encontrados durante a estação reprodutiva (variando entre 0,37 e 1,84 indivíduos/ha). Flutuações na densidade populacional podem apontar migrações altitudinais motivadas por variações na disponibilidade de recursos alimentares. Concluímos que o comportamento reprodutivo de L. lanioides não se enquadra no conceito de sistema reprodutivo em leks, conhecido em outros cotingídeos (ex. Lipaugus vociferans), no qual a corte é um comportamento social, com disputa por status de dominância, e o papel do macho resume-se à cópula sem benefícios diretos para as fêmeas. Dessa forma, os resultados do presente estudo trazem informações originais sobre a biologia de L. lanioides

Gaussian Process Vine Copulas for Multivariate Dependence

Copulas allow to learn marginal distributions separately from the multivariate dependence structure (copula) that links them together into a density function. Vine factorizations ease the learning of high-dimensional copulas by constructing a hierarchy of conditional bivariate copulas. However, to simplify inference, it is common to assume that each of these conditional bivariate copulas is independent from its conditioning variables. In this paper, we relax this assumption by discovering the latent functions that specify the shape of a conditional copula given its conditioning variables We learn these functions by following a Bayesian approach based on sparse Gaussian processes with expectation propagation for scalable, approximate inference. Experiments on real-world datasets show that, when modeling all conditional dependencies, we obtain better estimates of the underlying copula of the data.

Modelling of turbulent lifted jet flames using flamelets: A priori assessment and a posteriori validation

This study focuses on the modelling of turbulent lifted jet flames using flamelets and a presumed Probability Density Function (PDF) approach with interest in both flame lift-off height and flame brush structure. First, flamelet models used to capture contributions from premixed and non-premixed modes of the partially premixed combustion in the lifted jet flame are assessed using a Direct Numerical Simulation (DNS) data for a turbulent lifted hydrogen jet flame. The joint PDFs of mixture fraction Z and progress variable c, including their statistical correlation, are obtained using a copula method, which is also validated using the DNS data. The statistically independent PDFs are found to be generally inadequate to represent the joint PDFs from the DNS data. The effects of Z-c correlation and the contribution from the non-premixed combustion mode on the flame lift-off height are studied systematically by including one effect at a time in the simulations used for a posteriori validation. A simple model including the effects of chemical kinetics and scalar dissipation rate is suggested and used for non-premixed combustion contributions. The results clearly show that both Z-c correlation and non-premixed combustion effects are required in the premixed flamelets approach to get good agreement with the measured flame lift-off heights as a function of jet velocity. The flame brush structure reported in earlier experimental studies is also captured reasonably well for various axial positions. It seems that flame stabilisation is influenced by both premixed and non-premixed combustion modes, and their mutual influences. © 2014 Taylor & Francis.

Latent Stick-Breaking Processes.

We develop a model for stochastic processes with random marginal distributions. Our model relies on a stick-breaking construction for the marginal distribution of the process, and introduces dependence across locations by using a latent Gaussian copula model as the mechanism for selecting the atoms. The resulting latent stick-breaking process (LaSBP) induces a random partition of the index space, with points closer in space having a higher probability of being in the same cluster. We develop an efficient and straightforward Markov chain Monte Carlo (MCMC) algorithm for computation and discuss applications in financial econometrics and ecology. This article has supplementary material online.

Microscopical evaluation of neural connectivity between paired stages of Eudiplozoon nipponicum (Monogenea : Diplozoidae)

Diplozoidae monogeneans are fish-gill ectoparasites comprising 2 individuals fused in so-called permanent copula. This unique situation occurs when 2 larvae (diporpae) make contact on the host gill, such that their union triggers maturation into an individual adult worm. The present study examined paired stages of Eudiplozoon nipponicum microscopically to ascertain whether somatic fusion involves neural connectivity between these 2 heterogenic larvae. Neuronal pathways were demonstrated in whole-mount preparations of the worm, using indirect immunocytochemical techniques interfaced with confocal scanning laser microscopy for peptidergic and serotoninergic innervations and enzyme cytochemical methodology and light microscopy for cholinergic components. Elements of the central nervous systems of paired worms are connected by commissures the region of fusion so that the 2 systems are in structural continuity. Interindividual connections were most apparent between corresponding ventral nerve cords. All 3 classes of neuronal mediators were identified throughout both central and peripheral connections of the 2 nervous systems. The anatomical complexity and apparent plasticity of the diplozoon nervous system suggest that it has a pivotal role not only in motility, feeding, and reproductive behaviors but also in the events of larval pairing and somatic fusion.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Adjusting HIV Prevalence Estimates for Non-participation: an Application to Demographic Surveillance

Introduction: HIV testing is a cornerstone of efforts to combat the HIV epidemic, and testing conducted as part of surveillance provides invaluable data on the spread of infection and the effectiveness of campaigns to reduce the transmission of HIV. However, participation in HIV testing can be low, and if respondents systematically select not to be tested because they know or suspect they are HIV positive (and fear disclosure), standard approaches to deal with missing data will fail to remove selection bias. We implemented Heckman-type selection models, which can be used to adjust for missing data that are not missing at random, and established the extent of selection bias in a population-based HIV survey in an HIV hyperendemic community in rural South Africa.

Methods: We used data from a population-based HIV survey carried out in 2009 in rural KwaZulu-Natal, South Africa. In this survey, 5565 women (35%) and 2567 men (27%) provided blood for an HIV test. We accounted for missing data using interviewer identity as a selection variable which predicted consent to HIV testing but was unlikely to be independently associated with HIV status. Our approach involved using this selection variable to examine the HIV status of residents who would ordinarily refuse to test, except that they were allocated a persuasive interviewer. Our copula model allows for flexibility when modelling the dependence structure between HIV survey participation and HIV status.

Results: For women, our selection model generated an HIV prevalence estimate of 33% (95% CI 27–40) for all people eligible to consent to HIV testing in the survey. This estimate is higher than the estimate of 24% generated when only information from respondents who participated in testing is used in the analysis, and the estimate of 27% when imputation analysis is used to predict missing data on HIV status. For men, we found an HIV prevalence of 25% (95% CI 15–35) using the selection model, compared to 16% among those who participated in testing, and 18% estimated with imputation. We provide new confidence intervals that correct for the fact that the relationship between testing and HIV status is unknown and requires estimation.

Conclusions: We confirm the feasibility and value of adopting selection models to account for missing data in population-based HIV surveys and surveillance systems. Elements of survey design, such as interviewer identity, present the opportunity to adopt this approach in routine applications. Where non-participation is high, true confidence intervals are much wider than those generated by standard approaches to dealing with missing data suggest.

Automatic extraction of definitions

Tese de doutoramento, Informática (Engenharia Informática), Universidade de Lisboa, Faculdade de Ciências, 2014

Cappadocia: where Greek prepositions come to die

The Cappadocian variety of Ulaghátsh is unique among the Greek-speaking world in having lost the inherited preposition ‘se’. The innovation is found with both locative and allative uses and has af-ected both syntactic contexts in which ‘se’ was originally found, that is, as a simple preposition (1) and as the left-occurring member of circumpositions of the type ‘se’ + NP + spatial adverb (2). (1) a. tránse ci [to meidán] en ávʝa see.PST.3SG COMP ART.DEF.SG.ACC yard.SG.ACC COP.3 game.PL.NOM ‘he saw that in the yard is some game’ (Dawkins 1916: 348) b. ta erʝó da qardáʃa évɣan [to qonáq] ART.DEF.PL.NOM two ART.DEF.PL.NOM friend.PL.NOM ascend.PST.3PL ART.DEF.SG.ACC house.SG.ACC ‘the two friends went up to the house’ (Dawkins 1916: 354) (2) émi [ta qonáca mésa], kiríʃde [to ʝasdɯ́q píso] enter.PST.3SG ART.DEF.PL.NOM house.PL.ACC inside hide.PST.3SG. ART.DEF.SG.ACC cushion.SG.ACC behind ‘he went into the houses and hid behind the cushions’ (Dawkins 1916: 348) In this paper, we set out to provide (a) a diachronic account of the loss of ‘se’ in Asia Minor Greek, and (b) a synchronic analysis of its ramifications for the encoding of the semantic and grammatical functions it had prior to its loss. The diachronic development of ‘se’ is traced by comparing the Ulaghátsh data with those obtained from Cappadocian varieties that have neither lost it nor do they show signs of losing it and, crucially, also from varieties in which ‘se’ is in the process of being lost. The comparative analysis shows that the loss first became manifest in circumpositions in which ‘se’ was preposed to the complement to which in turn a wide range of adverbs expressing topological relations were postposed (émi sa qonáca mésa > émi ta qonáca mésa). This finding is accounted for in terms of Sinha and Kuteva’s (1995) distributed spatial semantics framework, which accepts that the elements involved in the constructions under investigation—the verb (émi), ‘se’ and the spatial adverb (mésa)—all contribute to the expression of the spatial relational meaning but with differences in weighting. Of the three, ‘eis’ made the most minimal contribution, the bulk of it being distributed over the verb and the adverb. This allowed for it to be optionally dropped from circumpositions, a stage attested in Phlo-tá Cappadocian and Silliot, and to be later completely abandoned, originally in allative and subsequently in locative contexts (earlier: évɣan so qonáq > évɣan to qonáq; later: so meidán en ávʝa > to meidán en ávʝa). The earlier loss in allative contexts is also dealt with in distributed semantics terms as verbs of motion such as έβγαν are semantically more loaded than vacuous verbs like the copula and therefore the preposition could be left out in the former context more easily than in the latter. The analysis also addresses the possibility that the loss of ‘se’ may ultimately originate in substandard forms of Medieval Greek, which according to Tachibana (1994) displayed SPATIAL ADVERB + NP constructions. Applying the semantic map model (Croft 2003, Haspelmath 2003), the synchronic analysis of the varieties that retain ‘se’ reveals that—like many other allative markers crosslinguistically—it displays a pattern of multifunctionality in expressing nine different functions (among others allative, locative, recipient, addressee, experiencer), which can be mapped against four domains, viz. the spatiotemporal, the social, the mental and the logicotextual (cf. Rice & Kabata 2007). In Ulaghátsh Cappadocian, none of these functions is overtly marked as such. In cases like (1), the intended spatial relational meaning is arrived at through the combination of the syntax and the inherent semantics of the verb and the zero-marked NP as well as from the context. In environments of the type exemplified by (2), the adverb contributes further to the correct interpretation. The analysis additionally shows that, despite the loss of ‘se’, Ulaghátsh patterns with all other Cappadocian varieties in one important aspect: Goal and Location are expressed similarly (by zero in Ulaghátsh, by ‘se’ in the other varieties) whereas Source is being kept distinct (expressed by ‘apó’ in all varieties). Goal-Location polysemy is very common across the world’s languages and, most crucially, prevails over other possible polysemies in the tripartite distinction Source—Location—Goal (Lestrade 2010, Nikitina 2009). Taking into account this empirical observation, our findings suggest that the reor-anisation of spatial systems can have a local effect—in our case the loss of a member of the prepositional paradigm—but will keep the original global picture intact, thus conforming to crosslinguistically robust tendencies.  References Croft, W. 2001. Radical Construction Grammar: Syntactic Theory in Typological Perspective. Oxford: Oxford University Press. Dawkins, R. M. 1916. Modern Greek in Asia Minor: A Study of the Dialects of Sílli, Cappadocia and Phárasa with Grammar, Texts, Translations and Glossary. Cambridge: Cambridge University Press. Haspelmath, M. 2003. The geometry of grammatical meaning: semantic maps and cross-linguistic comparison. In M. Tomasello (Ed.), The New Psychology of Language, Volume 2. New York: Erlbaum, 211–243. Lestrade, S. 2010. The Space of Case. Doctoral dissertation. Radboud University Nijmegen. Nikitina, T. 2009. Subcategorization pattern and lexical meaning of motion verbs: a study of the source/goal ambiguity. Linguistics 47, 1113–1141. Rice, S. & K. Kabata. 2007. Cross-linguistic grammaticalization patterns of the allative. Linguistic Typology 11, 451–514. Sinha, C. & T. Kuteva. 1995. Distributed spatial semantics. Nordic Journal of Linguistics 18:2, 167–199. Tachibana, T. 1994. Syntactic structure of spatial expressions in the “Late Byzantine Prose Alexander Romance”. Propylaia 6, 35–51.

Reproduction in the temperate crayfish, Orconectes rusticus: intermale aggression, copulatary behaviour, and sperm competition

The chelipeds of Orconectes rusticus are sexually dimorphic; males possessing the larger. Males use their chelae in intermale aggressive interactions, both to threaten, and assault opponents. In dyadic interactions males with larger chelae were dominant over otherwise physically similar opponents. A high frequency of attack behaviour, coupled with a low frequency of threats during these interactions indicates that actual physical contact is required for opponent assessment. Large clawed males oriented females into the copulatory position faster than small clawed males. Females more frequently escaped the precopulatory-grasp attempts of small clawed males. Additionally, male-female pairs that included a large clawed male remained in copula longer than pairs that included a small clawed male. Sperm of the second male to mate took precedence over the sperm of the primary male. Sperm precedence was incomplete; about 900/0 paternity accrued to the second male.

Modélisation bayésienne des changements aux niches écologiques causés par le réchauffement climatique

Cette thèse présente des méthodes de traitement de données de comptage en particulier et des données discrètes en général. Il s'inscrit dans le cadre d'un projet stratégique du CRNSG, nommé CC-Bio, dont l'objectif est d'évaluer l'impact des changements climatiques sur la répartition des espèces animales et végétales. Après une brève introduction aux notions de biogéographie et aux modèles linéaires mixtes généralisés aux chapitres 1 et 2 respectivement, ma thèse s'articulera autour de trois idées majeures. Premièrement, nous introduisons au chapitre 3 une nouvelle forme de distribution dont les composantes ont pour distributions marginales des lois de Poisson ou des lois de Skellam. Cette nouvelle spécification permet d'incorporer de l'information pertinente sur la nature des corrélations entre toutes les composantes. De plus, nous présentons certaines propriétés de ladite distribution. Contrairement à la distribution multidimensionnelle de Poisson qu'elle généralise, celle-ci permet de traiter les variables avec des corrélations positives et/ou négatives. Une simulation permet d'illustrer les méthodes d'estimation dans le cas bidimensionnel. Les résultats obtenus par les méthodes bayésiennes par les chaînes de Markov par Monte Carlo (CMMC) indiquent un biais relatif assez faible de moins de 5% pour les coefficients de régression des moyennes contrairement à ceux du terme de covariance qui semblent un peu plus volatils. Deuxièmement, le chapitre 4 présente une extension de la régression multidimensionnelle de Poisson avec des effets aléatoires ayant une densité gamma. En effet, conscients du fait que les données d'abondance des espèces présentent une forte dispersion, ce qui rendrait fallacieux les estimateurs et écarts types obtenus, nous privilégions une approche basée sur l'intégration par Monte Carlo grâce à l'échantillonnage préférentiel. L'approche demeure la même qu'au chapitre précédent, c'est-à-dire que l'idée est de simuler des variables latentes indépendantes et de se retrouver dans le cadre d'un modèle linéaire mixte généralisé (GLMM) conventionnel avec des effets aléatoires de densité gamma. Même si l'hypothèse d'une connaissance a priori des paramètres de dispersion semble trop forte, une analyse de sensibilité basée sur la qualité de l'ajustement permet de démontrer la robustesse de notre méthode. Troisièmement, dans le dernier chapitre, nous nous intéressons à la définition et à la construction d'une mesure de concordance donc de corrélation pour les données augmentées en zéro par la modélisation de copules gaussiennes. Contrairement au tau de Kendall dont les valeurs se situent dans un intervalle dont les bornes varient selon la fréquence d'observations d'égalité entre les paires, cette mesure a pour avantage de prendre ses valeurs sur (-1;1). Initialement introduite pour modéliser les corrélations entre des variables continues, son extension au cas discret implique certaines restrictions. En effet, la nouvelle mesure pourrait être interprétée comme la corrélation entre les variables aléatoires continues dont la discrétisation constitue nos observations discrètes non négatives. Deux méthodes d'estimation des modèles augmentés en zéro seront présentées dans les contextes fréquentiste et bayésien basées respectivement sur le maximum de vraisemblance et l'intégration de Gauss-Hermite. Enfin, une étude de simulation permet de montrer la robustesse et les limites de notre approche.

Densités de copules archimédiennes hiérarchiques

Les copulas archimédiennes hiérarchiques ont récemment gagné en intérêt puisqu’elles généralisent la famille de copules archimédiennes, car elles introduisent une asymétrie partielle. Des algorithmes d’échantillonnages et des méthodes ont largement été développés pour de telles copules. Néanmoins, concernant l’estimation par maximum de vraisemblance et les tests d’adéquations, il est important d’avoir à disposition la densité de ces variables aléatoires. Ce travail remplie ce manque. Après une courte introduction aux copules et aux copules archimédiennes hiérarchiques, une équation générale sur les dérivées des noeuds et générateurs internes apparaissant dans la densité des copules archimédiennes hiérarchique. sera dérivée. Il en suit une formule tractable pour la densité des copules archimédiennes hiérarchiques. Des exemples incluant les familles archimédiennes usuelles ainsi que leur transformations sont présentés. De plus, une méthode numérique efficiente pour évaluer le logarithme des densités est présentée.

Les modèles vectoriels et multiplicatifs avec erreurs non-négatives de séries chronologiques.

L'objectif du présent mémoire vise à présenter des modèles de séries chronologiques multivariés impliquant des vecteurs aléatoires dont chaque composante est non-négative. Nous considérons les modèles vMEM (modèles vectoriels et multiplicatifs avec erreurs non-négatives) présentés par Cipollini, Engle et Gallo (2006) et Cipollini et Gallo (2010). Ces modèles représentent une généralisation au cas multivarié des modèles MEM introduits par Engle (2002). Ces modèles trouvent notamment des applications avec les séries chronologiques financières. Les modèles vMEM permettent de modéliser des séries chronologiques impliquant des volumes d'actif, des durées, des variances conditionnelles, pour ne citer que ces applications. Il est également possible de faire une modélisation conjointe et d'étudier les dynamiques présentes entre les séries chronologiques formant le système étudié. Afin de modéliser des séries chronologiques multivariées à composantes non-négatives, plusieurs spécifications du terme d'erreur vectoriel ont été proposées dans la littérature. Une première approche consiste à considérer l'utilisation de vecteurs aléatoires dont la distribution du terme d'erreur est telle que chaque composante est non-négative. Cependant, trouver une distribution multivariée suffisamment souple définie sur le support positif est plutôt difficile, au moins avec les applications citées précédemment. Comme indiqué par Cipollini, Engle et Gallo (2006), un candidat possible est une distribution gamma multivariée, qui impose cependant des restrictions sévères sur les corrélations contemporaines entre les variables. Compte tenu que les possibilités sont limitées, une approche possible est d'utiliser la théorie des copules. Ainsi, selon cette approche, des distributions marginales (ou marges) peuvent être spécifiées, dont les distributions en cause ont des supports non-négatifs, et une fonction de copule permet de tenir compte de la dépendance entre les composantes. Une technique d'estimation possible est la méthode du maximum de vraisemblance. Une approche alternative est la méthode des moments généralisés (GMM). Cette dernière méthode présente l'avantage d'être semi-paramétrique dans le sens que contrairement à l'approche imposant une loi multivariée, il n'est pas nécessaire de spécifier une distribution multivariée pour le terme d'erreur. De manière générale, l'estimation des modèles vMEM est compliquée. Les algorithmes existants doivent tenir compte du grand nombre de paramètres et de la nature élaborée de la fonction de vraisemblance. Dans le cas de l'estimation par la méthode GMM, le système à résoudre nécessite également l'utilisation de solveurs pour systèmes non-linéaires. Dans ce mémoire, beaucoup d'énergies ont été consacrées à l'élaboration de code informatique (dans le langage R) pour estimer les différents paramètres du modèle. Dans le premier chapitre, nous définissons les processus stationnaires, les processus autorégressifs, les processus autorégressifs conditionnellement hétéroscédastiques (ARCH) et les processus ARCH généralisés (GARCH). Nous présentons aussi les modèles de durées ACD et les modèles MEM. Dans le deuxième chapitre, nous présentons la théorie des copules nécessaire pour notre travail, dans le cadre des modèles vectoriels et multiplicatifs avec erreurs non-négatives vMEM. Nous discutons également des méthodes possibles d'estimation. Dans le troisième chapitre, nous discutons les résultats des simulations pour plusieurs méthodes d'estimation. Dans le dernier chapitre, des applications sur des séries financières sont présentées. Le code R est fourni dans une annexe. Une conclusion complète ce mémoire.

Sur les prolongements de sous-copules

L’objet du travail est d’étudier les prolongements de sous-copules. Un cas important de l’utilisation de tels prolongements est l’estimation non paramétrique d’une copule par le lissage d’une sous-copule (la copule empirique). Lorsque l’estimateur obtenu est une copule, cet estimateur est un prolongement de la souscopule. La thèse présente au chapitre 2 la construction et la convergence uniforme d’un estimateur bona fide d’une copule ou d’une densité de copule. Cet estimateur est un prolongement de type copule empirique basé sur le lissage par le produit tensoriel de fonctions de répartition splines. Le chapitre 3 donne la caractérisation de l’ensemble des prolongements possibles d’une sous-copule. Ce sujet a été traité par le passé; mais les constructions proposées ne s’appliquent pas à la dépendance dans des espaces très généraux. Le chapitre 4 s’attèle à résoudre le problème suivant posé par [Carley, 2002]. Il s’agit de trouver la borne supérieure des prolongements en dimension 3 d’une sous-copule de domaine fini.