Paris West University Nanterre La Défense

About: Paris West University Nanterre La Défense is a education organization based out in Paris, France. It is known for research contribution in the topics: Population & Finite element method. The organization has 895 authors who have published 1430 publications receiving 21712 citations.

Dettes souveraines : limites du traitement keynesien d'une crise structurelle

Abstract: Why were several years of stimulation of demand by very large fiscal deficits not sufficient to allow the economies of the old centres (the United States and Europe) to recover their autonomous capability to grow? From this lack of capability results the contradictory character of the present situation On the one hand, the deficits are still required in order to maintain the general level of activity; on the other hand, the unbounded growth of government debts seems impossible to prolong This impasse manifests the “structural character” of the crisis, one of the large phases of perturbation that, every thirty or forty years, punctuate the history of capitalism and compel it to transform itself in fundamental respects, into what we denote as new “social orders” The resolution of the circumstances of the present crisis requires much more than macro policies Involved are economic institutions, the management of enterprises, the function of the financial sector, industrial policies and international relations The crisis highlights the negative impact of neoliberal practices, leading to the deindustrialization of the economies of the centre, establishing a new configuration of growth around the globe Leaving aside certain obvious singularities, the peripheries are now growing more rapidly than the centre

A Riemannian Framework for Low-Rank Structured Elliptical Models

Abstract: This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is the one induced by the product of the Stiefel manifold and the manifold of Hermitian positive definite matrices, quotiented by the unitary group. One of the main contribution is to consider an original Riemannian metric, leading to new representations of tangent spaces and geodesics. From this geometry, we derive a new Riemannian optimization framework for robust covariance estimation, which is leveraged to minimize the popular Tyler's cost function on the considered quotient manifold. We also obtain a new divergence function, which is exploited to define a geometrical error measure on the quotient, and the corresponding intrinsic Cram\'er-Rao lower bound is derived. Thanks to the structure of the chosen parametrization, we further consider the subspace estimation error on the Grassmann manifold and provide its intrinsic Cram\'er-Rao lower bound. Our theoretical results are illustrated on some numerical experiments, showing the interest of the proposed optimization framework and that performance bounds can be reached.

On the Asymptotics of Maronna's Robust PCA

Abstract: The eigenvalue decomposition (EVD) parameters of the second order statistics are ubiquitous in statistical analysis and signal processing. Notably, the EVD of the $M$ -estimators of the scatter matrix is a popular choice to perform robust probabilistic PCA or other dimension reduction related applications. Towards the goal of characterizing this process, this paper derives new asymptotics for the EVD parameters (i.e. eigenvalues, eigenvectors, and principal subspace) of $M$ -estimators in the context of complex elliptically symmetric distributions. First, their Gaussian asymptotic distribution is obtained by extending standard results on the sample covariance matrix in the Gaussian context. Second, their convergence towards the EVD parameters of a Gaussian-Core Wishart Equivalent is derived. This second result represents the main contribution in the sense that it quantifies when it is acceptable to directly rely on well-established results on the EVD of Wishart-distributed matrix for characterizing the EVD of $M$ -estimators. Finally, some examples (intrinsic bias analysis, rank estimation, and low-rank adaptive filtering) illustrate where the obtained results can be leveraged.

Legitimacy of Legislative and Executive Actions of International Institutions

Abstract: I have been kindly asked by the organizers of this Symposium to deal with a vast, difficult and, possibly, impossible topic. This is why I will first explain why I will not deal with my assigned topic. Then I will try to deal with it. And finally, if time and your patience allow, I will try to draw some conclusions — here again wider than my assigned topic.