1,721,063 research outputs found
Théorèmes limites pour des champs aléatoires dépendants et applications
No full textCette thèse est consacrée au théorème central limite (TCL) et à sa version fonctionnelle pour les champs aléatoires strictement stationnaires. Dans un premier temps, nous traiterons des champs aléatoires strictement stationnaires non nécessairement adaptés à la filtration naturelle, et lorsque la variance asymptotique ne croit pas nécessairement linéairement. Dans cette partie, nous donnons le TCL et sa version fonctionnelle pour les champs aléatoires strictement stationnaires sous la normalisation (sn)_{n dans Z^d}, où (sn)_{n dans Z^d} est une suites réels positifs qui tend vers infini quand n tend vers infini. Dans un deuxième temps, nous nous intéresserons à l'extension du TCL de Gordin sous une condition L^1 projective. On verra que dans le cadre des champs aléatoires indexés par Z^d avec d supérieur ou égal à 2, une condition supplémentaire par rapport au cadre des suites (d = 1) est nécessaire pour obtenir le TCL.Dans le dernier chapitre, nous nous intéresserons au comportement asymptotique des sommes partielles associées à des champs aléatoires à valeurs dans des espaces de Banach. En particulier nous établirons la version fonctionnelle du TCL pour les champs de différences d'ortho-martingales ergodiques et à valeurs dans un espace de Banach soit 2-lisse ou de cotype 2. Puis à l'aide d'une approximation ortho-martingale, nous obtiendrons une version fonctionnelle du TCL pour des champs aléatoires strictement stationnaires à valeurs dans un espace L^p, p dans [1,2], sous des critères projectifsThis thesis is devoted to the central limit theorem (CLT) and its functional version for strictly stationary random fields.In the first part, we deal with strictly stationary random fields that are not necessarily adapted to the natural filtration, and when the asymptotic variance does not necessarily grow linearly. In this part, we give the CLT and its functional version for strictly stationary random fields under the normalization (sn)_{n inZ^d}, where (sn)_{n inZ^d} is a sequence of positive reals which tends to infinity when n tends to infinity.In the second part, we are interested in the extension of Gordin's CLT under a projective L^1 condition. We will see that for random fields indexed by Z^d with d greater than or equal to 2, an additional condition with respect to sequences (d = 1) is necessary in order to obtain the CLT.In the last part, we are interested in the asymptotic behavior of partial sums associated to random fields with values in Banach spaces. In Particular, we obtained the functional version of the CLT for fields of ortho-martingales differences that are ergodic and take values in a 2-smooth or cotype 2 Banach space. Then, using an ortho-martingale approximation, we derive a functional version of the CLT for strictly stationary random fields with values in a L^p space, p in [1,2], under projetive cirteri
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Asymptotics and fluctuations of largest eigenvalues of empirical covariance matrices associated with long memory stationary processes
No full textLes grandes matrices de covariance constituent certainement l’un des modèles les plus utiles pour les applications en statistiques en grande dimension, en communication numérique, en biologie mathématique, en finance, etc. Les travaux de Marcenko et Pastur (1967) ont permis de décrire le comportement asymptotique de la mesure spectrale de telles matrices formées à partir de N copies indépendantes de n observations d’une suite de variables aléatoires iid et sa convergence vers une distribution de probabilité déterministe lorsque N et n convergent vers l’infini à la même vitesse. Plus récemment, Merlevède et Peligrad (2016) ont démontré que dans le cas de grandes matrices de covariance issues de copies indépendantes d’observations d’un processus strictement stationnaire centré, de carré intégrable et satisfaisant des conditions faibles de régularité, presque sûrement, la distribution spectrale empirique convergeait étroitement vers une distribution non aléatoire ne dépendant que de la densité spectrale du processus sous-jacent. En particulier, si la densité spectrale est continue et bornée (ce qui est le cas des processus linéaires dont les coefficients sont absolument sommables), alors la distribution spectrale limite a un support compact. Par contre si le processus stationnaire exhibe de la longue mémoire (en particulier si les covariances ne sont pas absolument sommables), le support de la loi limite n'est plus compact et des études plus fines du comportement des valeurs propres sont alors nécessaires. Ainsi, cette thèse porte essentiellement sur l’étude des asymptotiques et des fluctuations des plus grandes valeurs propres de grandes matrices de covariance associées à des processus stationnaires à longue mémoire. Dans le cas où le processus stationnaire sous-jacent est Gaussien, l’étude peut être simplifiée via un modèle linéaire dont la matrice de covariance de population sous-jacente est une matrice de Toeplitz hermitienne. On montrera ainsi que dans le cas de processus stationnaires gaussiens à longue mémoire, les fluctuations des plus grandes valeurs propres de la grande matrice de covariance empirique convenablement renormalisées sont gaussiennes. Ce comportement indique une différence significative par rapport aux grandes matrices de covariance empirique issues de processus à courte mémoire, pour lesquelles les fluctuations de la plus grande valeur propre convenablement renormalisée suivent asymptotiquement la loi de Tracy-Widom. Pour démontrer notre résultat de fluctuations gaussiennes, en plus des techniques usuelles de matrices aléatoires, une étude fine du comportement des valeurs propres et vecteurs propres de la matrice de Toeplitz sous-jacente est nécessaire. On montre en particulier que dans le cas de la longue mémoire, les m plus grandes valeurs propres de la matrice de Toeplitz convergent vers l’infini et satisfont une propriété de type « trou spectral multiple ». Par ailleurs, on démontre une propriété de délocalisation de leurs vecteurs propres associés. Dans cette thèse, on s’intéresse également à l’universalité de nos résultats dans le cas du modèle simplifié ainsi qu’au cas de grandes matrices de covariance lorsque les matrices de Toeplitz sont remplacées par des matrices diagonales par blocsLarge covariance matrices play a fundamental role in the multivariate analysis and high-dimensional statistics. Since the pioneer’s works of Marcenko and Pastur (1967), the asymptotic behavior of the spectral measure of such matrices associated with N independent copies of n observations of a sequence of iid random variables is known: almost surely, it converges in distribution to a deterministic law when N and n tend to infinity at the same rate. More recently, Merlevède and Peligrad (2016) have proved that in the case of large covariance matrices associated with independent copies of observations of a strictly stationary centered process which is square integrable and satisfies some weak regularity assumptions, almost surely, the empirical spectral distribution converges weakly to a nonrandom distribution depending only on the spectral density of the underlying process. In particular, if the spectral density is continuous and bounded (which is the case for linear processes with absolutely summable coefficients), the limiting spectral distribution has a compact support. However, if the underlying stationary process exhibits long memory, the support of the limiting distribution is not compact anymore and studying the limiting behavior of the eigenvalues and eigenvectors of the associated large covariance matrices can give more information on the underlying process. This thesis is in this direction and aims at studying the asymptotics and the fluctuations of the largest eigenvalues of large covariance matrices associated with stationary processes exhibiting long memory. In the case where the underlying stationary process is Gaussian, the study can be simplified by a linear model whose underlying population covariance matrix is a Hermitian Toeplitz matrix. In the case of stationary Gaussian processes exhibiting long memory, we then show that the fluctuations of the largest eigenvalues suitably renormalized are Gaussian. This limiting behavior shows a difference compared to the one when large covariance matrices associated with short memory processes are considered. Indeed in this last case, the fluctuations of the largest eigenvalues suitably renormalized follow asymptotically the Tracy-Widom law. To prove our results on Gaussian fluctuations, additionally to usual techniques developed in random matrices analysis, a deep study of the eigenvalues and eigenvectors behavior of the underlying Toeplitz matrix is necessary. In particular, we show that in the case of long memory, the largest eigenvalues of the Toeplitz matrix converge to infinity and satisfy a property of “multiple spectral gaps”. Moreover, we prove a delocalization property of their associated eigenvectors. In this thesis, we are also interested in the universality of our results in the case of the simplified model and also in the case of large covariance matrices when the Toeplitz matrices are replaced by bloc diagonal matrice
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On strong approximations for some classes of random iterates
No full texthis talk is devoted to strong approximations in the dependent setting. The famous results of Koml\'os, Major and Tusn\'ady (1975-1976) state that it
is possible to approximate almost surely the partial sums of size of i.i.d. centered random
variables in () by a Wiener process with an
error term of order . In the case of functions of random iterates generated by an iid sequence, we
we shall give new dependent conditions, expressed in terms of a natural coupling (in or in ), under which the strong approximation result holds with rate
. The proof is an adaptation of the recent construction given in Berkes, Liu and Wu (2014).
As we shall see our conditions are well adapted to a large variety of models, including left random
walks on , contracting iterated random functions, autoregressive Lipschitz processes, and some ergodic Markov chains.
We shall also provide some examples showing that our -coupling condition is in some sense optimal. This talk is based on a joint work with J. Dedecker and C. Cuny.Non UBCUnreviewedAuthor affiliation: University Paris Est Marne-la-ValléeFacult
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Central limit theorem for linear processes with values in a Hilbert space
No full textAbstractIn this paper we study the behavior of Sn = ∑nk = 1αnkεk associated to an i.i.d. sequence (εk, k ∈ Z) with values in a real separable Hilbert space H of infinite dimension, and where (αnk, 1 ⩽ k ⩽ n) is a triangular array of bounded linear operators from H to H. We shall provide sufficient conditions for the CLT for (Sn, n ⩾ 1) imposed on the norm of the operators and on the moments of Sn
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